Consider the functions (x) = 3x² – x – 4 and g(x) = 2– 5x. Find (a) g(f(-4)) and (b) simplify completely an equation for f (g(x)). 21.

Q: Use the chain rule to find the derivative of  f(x)= 3(3x^10-6x^9)^17 You do not need to expand out…

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Q: Find the derivative of the function. f(x) = (2x³ – 8x?+ 7)1

A: topic - derivative of a function

Q: Find the second derivative of the function. f(x) = (3x5 + 6)6

A: topic - double derivative

Q: Find the derivative of the function f(x) = (5x^4)/12

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Q: Find the derivative of the function.

A: fx=x3-2x+3x-3

Q: use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

A: y = (x4 − x3 − 1)2/3 derivative formula ddxxn=nxn-1

Q: Find the derivative of f(x) = -4x ( 3' *(3"). %D 3+4

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Q: The derivative of f(x) =3 4 is %3D

A: Consider the given function, fx=4x5 The property of derivative is defined as, ddxxn=nxn-1 Convert…

Q: For the function f(x)=2x^3-12x^2+20, Use the SECOND DERIVATIVE TEST to find the relative extrema.

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Q: f (x) = 3 · 5" + e 4x²+7¤

A: We have to find derivative

Q: Question 2

A: f'(x)= 64(54x5 -27x2 ) (9x6-9x3)16

Q: Match the function from the left side to its derivative. 1. x16 -4x-5 3 a. 2. 15 b. 3. ** 15x4 с.

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Q: Find the second derivative of the function. f (x) = 5(2 – 7x)*

A: Find the second derivative of the function

Q: Find the second derivative of the function. f(x)= (3x³+6)* %D

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Q: Find the derivative of the function.    t(x) = (x2 − 8x3)/(x)

A: Given, t(x)=x2-8x3xTake 'x' common from numerator,we gett(x)=xx-8x2xCancel 'x' from both numerator…

Q: For f(x) = (2a* + 3x)(5x*), find the derivative of f(x). 80x7+ 60x3 20x7-30a3 O 10z8 + 15x4 O…

A: We will use concept of differentiation to solve this.

Q: Use the Quotient Rule to find the derivative of the function. 5x - 8 23TOM YM x2 – 1 g(x) = g'(x) =…

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Q: Find the derivative of the function. y = 3√(6x2 + 1)

A: y=36x2+1

Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

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Q: Find the derivative of the function f(x) (3x+6)? 6x2+13

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Q: Find the 3rd derivative of the functions: y = 12(5x2 –1)(x2 –1)

A: Find the 3rd derivative of the functions: Given y=12(5x2-1)(x2-1) To find dydx, d2ydx2, d3ydx3

Q: Find the derivative of the function. r (x) = 3x 20.6 8. -8 - 6. 6x1.6 2]

A: The derivative of a polynomial function with degree n:

Q: Jx + 2x f(x)=- 7х — 4х? 8.

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Q: Use the chain rule to find the derivative of f(x)=5e^(3x^9−6x^10) f'(x)=____

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Q: Use the chain rule to find the derivative of f(x) = 2( – 72* – 8z*) 4 You do not need to expand out…

A: Given: f(x)= 2(-7x8-8x5)14

Q: Use the chain rule to find the derivative of 16 f(x) = 3( – 52° – 9x")" You do not need to expand…

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Q: Use the chain rule to find the derivative of 16 f(x) = 3(8r" - 5z ) * You do not need to expand out…

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Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: Use the chain rule to find the derivative of 15 f(x) = 4( – 2a + 10x')" You do not need to expand…

A: We can find the derivative using chain rule as below

Q: Find the second derivative for the function f (x) = 4e . 1 - 2x3

A: Given: fx=4ex-12x3 for finding second derivative of given, we find first derivative then find…

Q: Find the derivative of f(x)= 5x2 (4+5e")?

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Q: Use the chain rule to find the derivative of f(x)=4(5x^5+2x^4)^−1/2 The answer should look like…

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Q: Find the derivative of the functionf(x)= 9x² + 4x +6, using the definition of the derivative,

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Q: Find the second derivative of the function. f(x)= [3x3+7]7

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Q: f(x) = (x + 2)(2x² – 3) %3D

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Q: Use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

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Q: Find the value of x for which the derivative is zero. y=x3+4x2-3x-5

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Q: Find the derivative of the function. g(x) = 8/ (5x2-6x)4

A: To find the derivative of the function

Q: Use the chain rule to find the derivative of 5(– 3a10 – 9a*)5 3x10 You do not need to expand out…

A: Given that: y=5(-3x10-9x4)15

Q: Find the derivative of the function. F(x) = (x4 + 5x2 – 9)6

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Q: 3. f(x)=(3x' +2):

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Q: Find the derivative. y = e2= . 8x3 24x?e2 + 16x4e2« – 1 O 2e2a . 24x? 24x e2 + 16x³e2* O 2xe2a…

A: We will find the derivative using Chain rule.

Q: Use the Product Rule to find the derivative of the function. f(x)= (4x+ 7)(x² 8) а. 8х b. 2x + 4 c.…

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Q: Find the derivative of the function.

A: The given function is gx=3x2-22x+3-2.

Q: b) Find and simplify the derivative of the function below: y = x°(3x² + 1)*

A: Use the chain rule and power rule of derivative and simplify the result.

Q: Find the Derivative of the Function: 2x2 3 | f (x) 5x? 6

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Q: Find the derivative of the function. y = x3 - (x2)/(28) +8x + 5

A: The given function is: y = x3-x228+8x + 5 The derivative of xn is given by: dxndx=nxn-1 And, the…

Q: 4. Given the function y = 2x³ - 4x² + 5, find its derivative.

A: Differentiate with respect to x