The derivative of [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex] is [tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex].
In this question we shall use the following derivative rules:
Derivative of a sum of functions
[tex]\frac{d}{dt}(f(t) + g(t)) = \frac{df(t)}{dt} + \frac{dg(t)}{dt}[/tex] (1)
Derivative of a product of functions
[tex]\frac{d}{dt}(f(t)\cdot g(t)) = \frac{df(t)}{dt}\cdot g(t) + f(t)\cdot \frac{dg(t)}{dt}[/tex] (2)
Derivative of a constant
[tex]\frac{d}{dt}(k) = 0[/tex], [tex]\forall k \in \mathbb{R}[/tex] (3)
Derivative of a function multiplied by a constant
[tex]\frac{d}{dt}(c\cdot f(t)) = c\cdot \frac{df(t)}{dt}[/tex], [tex]\forall\, c\in \mathbb{R}[/tex] (4)
Derivative of the cosine function
[tex]\frac{d}{dt} \cos t = -\sin t[/tex] (5)
Derivative of the tangent function
[tex]\frac{d}{dt}\tan t = \sec^{2} t[/tex] (6)
Chain rule
[tex]\frac{d}{dt}f[u(t)] = \frac{df(u)}{du}\cdot \frac{du(t)}{dt}[/tex] (7)
Let be [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex], then the derivative of [tex]f(x)[/tex] is:
[tex]f'(x) = \sec^{2}x\cdot (4 + 3\cdot \cos x) + (3+\tan x)\cdot (-3\cdot \sin x)[/tex]
[tex]f'(x) = 4\cdot \sec^{2}x+3\cdot \sec x -9\cdot \sin x -3\cdot \sin x\cdot \tan x[/tex]
[tex]f'(x) = \frac{4+3\cdot \cos x}{\cos^{2}x} -\frac{9\cdot \sin x \cdot \cos x+3\cdot \sin^{2}x}{\cos x}[/tex]
[tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex]
The derivative of [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex] is [tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex].
We kindly invite to check this question on derivatives: https://brainly.com/question/21202620
find the slope of the line that passes through (6, 3) and (10, 6)
Step-by-step explanation:
3/4
insert 1st point into y=mx+b
3=m(6)+b
insert 2nd point into y=mx+b
6=m(10)+b
-----------------------------------
use system of equations to solve for m and b
b=3-6m
b=6-10m
3-6m=6-10m
4m=3
m=3/4
insert back into the equation
3=(3/4)6+b
3=9/2+b
3-9/2=b
-3/2=b
insert back into y=mx+b
m=slope
b=y-intercept
y=(3/4)x-3/2
slope=3/4
Hope that helps :)
Answer:slope=3/4
Step-by-step explanation:
Can you guys please help me i dont understand
file:///C:/Users/home/Desktop/Downloads/Ch%207.5%20Notes%20Writing%20and%20Graphing%20Inequalities.pdf
Answer:
It tells the anwser for some questions.
Step-by-step explanation:
Solve for x.
I need help on this
Answer:
x = 7
Step-by-step explanation:
2(x + 2) = 3x - 3
2x + 4 = 3x -3
x = 7
A package of 4 pair of insulated socks cost $32.76. What is the unit price of the pair of socks
Answer:
The answer is 8.19, You have to divide 32.76 by 4(Ps. Sorry I'm not good at explaining)
question is below
Answer:
45=9⋅5 , so 2√45 is the same as 2⋅√9⋅5 . The √9=3 , so a 3 can be removed. leaving 2⋅3√5 , or 6√5
Will mark brainliest, I just really need help w/ this!!!
Answer:
Step-by-step explanation:
1 and 6 are vertical angles.
HI THIS IS SUCH A SIMPLE QUESITON BUT MY BRAIN ISNT WORKING HELP
Answer:
It doesn't say, but I think it is 781.57
Step-by-step explanation:
Someone plz help meh
48 = 9x + 3
A) 5
B) -13
C) 8
D) -1
What is the standard form equation for this slope intercept equation?
y = -7x + 12
Answer: x=
−1
7
y+
12
7
Step-by-step explanation:
What the answer to this question 8 (x+5)
what are the prime numbers for 17
Answer:
17 is prime
Step-by-step explanation:
An apple pie that has a 9-inch diameter is cut into six pieces. Lucas takes one slice of pie and sprays whipped cream in an arc along the curved edge of his piece. What is the length of Logan's arc
of whipped cream?
A
4.71 in
B
9.42 in
С
18.8 in
D
10.6 in
Tony owes Tina 40p.
Then Tina borrows 50p from Tony.
Later Tony gives Tina 60p.
Who has to pay what to whom to
square things up?
nswer
I need to answer this challenge
i need help really bad because this is confusing
If two angles are supplementary, their sum equals
A)
45°
B)
90°
180°
D)
360°
Answer:
180°
Step-by-step explanation:
Supplementary angles are two angles whose sum is equal to 180∘. In other words when you add the measure of one angle in the pair with the other angle in the pair, they equal 180 degrees. These two angles are supplementary because together they form a straight line.
Hope it is helpful....Multiply each equation by a constant that would help to eliminate the y terms.
2x-5y = -21
3x-3y = -18
What are the resulting equations?
6x-15y = -63
- 15x+15y = 90
6x-15y = 63
-15x+15y = 90
6x-15y=-63
- 15x+ 15y = -90
EASY EXTRA POINTS HELP ASAP
Answer:
(1,-1)
Step-by-step explanation:
The intersection of the two lines
HELP URGENT BRAINLIEST
Given:
LMN is an equilateral triangle.
LM = LN = MN = 12 cm
To find:
The height of the triangle h.
Solution:
In a right angle triangle,
[tex]\sin \theta=\dfrac{Opposite}{Hypotenuse}[/tex]
[tex]\sin (60^\circ)=\dfrac{h}{12}[/tex]
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{h}{12}[/tex]
Multiply both sides by 12.
[tex]\dfrac{\sqrt{3}}{2}\times 12=\dfrac{h}{12}\times 12[/tex]
[tex]6\sqrt{3}=h[/tex]
Therefore, the height of the triangle is [tex]6\sqrt{3}[/tex] cm.
write 20x20 using an exponent
Step-by-step explanation:
20^2 because you are multiplying 20 two times
20×20=20², is the exponent form.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, we have,
20×20
=400
=20²
Hence, 20×20=20², is the exponent form.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ2
Isaac used 1/4 of an ounce of nuts to make 1/8 of a cake. How many ounces of nuts are needed to make one cake?
Answer:
2 ounces of nuts are needed to make one cake.
Step-by-step explanation:
if he uses 1.4 to make 1/8 of a cake, then you need to do it 8 times to make a full cake. Multiply 1/4 * 8 which is equal to 8/4 which simplifies to 2. This is your answer!
2 ounces of nuts are needed to make one cake.
Please help due today right now
Answer:
Find "f(6)" __-8__
Find x when "f(x)=2" __x=1__
Step-by-step explanation:
For the first part, we will substitute 6 into the f(x) to get "-2(6)+4" When simplified further, you get "-12+4" which is "-8"
For the second part we will substitute the two as the answer of f(x) "-2x+4=2" Simplifying this further we get "-2x=-2" This means that x=1
If a system of linear equations has no solution, then ______.
Answer:
Answer. Answer: A system of linear equation has no solution when the graphs are parallel.Step-by-step explanation:
what is the value of a in the equation ax + b = c
Answer:
a= (c-b)/x
Step-by-step explanation:
subtract b to both sides
divide x to both sides
leaving a by itself.
find x to the nearest tenth
What type of lines are shown on the graph on the right? Explain your answer.
Answer: Parallel lines
Step-by-step explanation:
These lines are Parallel due to the fact that they will never cross each other. Since they are both perfectly lined up with each other, this makes them Parallel.
Check the picture, and thanks for the help
Answer:
According to me the answer is 'c'
write the following ratio in its simplest for 64:18
Answer:
32 : 9
Step-by-step explanation:
To write a ratio in its simplest form , the numerator and denominator should be reduced by their common factor(s).
64 = 2 × 2 × 2 × 2 × 2 × 2
18 = 2 × 3 × 3
⇒ Common factor of 64 & 18 is 2.
So , reducing 64 & 18 by 2 gives :-
[tex]\frac{64 \div 2}{18 \div 2} = \frac{32}{9}[/tex]
∴ Hence , the simplest form is 32 : 9.
round 6,577 the nearest thousand
Answer: 7,000
Step-by-step explanation: the hundred was greater than 5 so we round up any number after whatever you are doing if it’s 5 or greater you round up
HELPPPPPPPPPPPPPPPPPP
Answer:
I think it's 72
Step-by-step explanation:
I hade add them
what is -2 to the 8th power
Answer:
-256
Step-by-step explanation:
Put a negative next to 2^8 and you'll get your answer.