Calculate the derivative and its application. (a) 2x3 – 4x2 +x – 33 -

Q: Find the derivative of the function. 4x² +9 %3D y'

A: Differentiate w.r.t to x

Q: A1) Using the definition of derivative, find the derivative of f(x) = x² + 7x + 7.

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Q: Find the derivative of the function. x² + 2 y = 2 – , - 2 -&x(x² + 2, y' = (2² – 2)4

A: Given: The function is, y=x2+2x2-27. The objective is to find the derivative of the function.

Q: Use the Chain Rule to find the derivative of the function. y = (2x² - 9)3

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Q: f(x) = 4x³ - 12x² + 36x 12. What is the value of the 2nd derivative of the

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Q: Find the derivative of the function. y = 6x2(4x2 − 8)

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Q: Using the definition, find the derivative of the simplest quadratic function y=x2.

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Q: Using the definition of derivative, find the derivative of f(x) = x² + 3x + 3.

A: Solution:

Q: 3x - 7x- 4 Find the derivative of y= .2

A: The objective of the question is derivative the given function.

Q: What is the derivative?  (3x-4)2(x3)

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Q: Find the derivative of the function. y = (2x – 5)*(8x² – 5)-3

A: Derivative denotes rate of change. According to product rule, ddxf(x)g(x)=ddxf(x)g(x)+ddxg(x)f(x)

Q: A1) Using the definition of derivative, find the derivative of f(x) = x2 + 8x + 8.

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

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Q: A1) Using the definition of derivative, find the derivative of f(x) = x² + 4x + 4.

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Q: Find the derivative of the function. Y=3x-7/8x+1

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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: x5/2+4 x3 y = 3

A: We have to find the derivative of the given expression: y=x52+4x3x3 Simplifying the given…

Q: x'-3x+5 3) y= x² +1

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Q: Find the derivative of the function. +8x+3 10) y = %3D

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Q: Find the derivative.

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Q: Find the derivative of the function. y = -2e - 5x²

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Q: Find the derivative of the function. y = 2  4√(9 − x2)

A: Given function: y=29-x24

Q: f(x)=2x2−16x+35 , the derivative of the following function using the definition of the derivative.

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Q: Plot the function fx) = x3- 2x2-10sin?x-e0.9x and its derivative for %3D -25x54 in one figure. Plot…

A: The given function is  f(x)=x3-2x2-10sin2(x)-e0.9x and so the differential of the function is ,…

Q: compute the derivative y = (2 + 9x2)3/2

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Q: 4x+1 b. g(x) 9х-2

A: Given : g(x)=4x+19x-2   To Find : Derivative of g(x) using definition   NOTE:If f(x)=uv  , where u…

Q: Find the derivative of the function Y=5x^2-8x-8x^-2

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Q: Calculate the derivative of the function. f(x) = (2x2 – 9)-1

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Q: Find the derivative of the function. y = 3elx2 + 8)3

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Q: find the derivative by using the definition of a derivativef(x)=4x^2+1

A: Formula used:The derivative of f(x) with respect to x is the function f'(x) is

Q: Find the derivative. [2x(x^6+1)^3]

A: Let y=2x(x6+1)3

Q: Find the derivative. a) (x-3)(x+2)(x^3) b) 9x^2(10x+4)

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Q: f(2) — V3х — 7

A: Solved using terms of derivative.

Q: f (x)=vx+2, a=6 it

A: Given function is  fx=x+27

Q: Find the derivative of the function y = 4x3- x2+6x-5

A: Find the derivative of the function      y = 4x3- x2+6x-5

Q: B. Apply the quotient rule to find the derivative 1. y 4-7x 3. y = 5- 3x

A: From the quotient rule of derivative we get Let,  y=uv where u and v is function of x then dydx=…

Q: Using the definition of derivative, find the derivative of f(x) = 22 + 6x + 6.

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Q: Use the derivative rules to find the derivative of y = (2x-7)? y = (3x²+1)" y= 3x(4-9x)4 y=(3+x)²…

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Q: x = -t4 – 5t – 3 2.

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Q: Find the derivative. y = 2x 4 - 6x 3 + 5

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Q: Find the derivative of f (x) = ( a ° – 5æ) (2² + 6x - 6).

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Q: B2(a): Using the definition of derivative, find the derivative of f(x) = x² + 7.

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Q: A1) Using the definition of derivative, find the derivative of f(x) = x² + 2x + 2.

A: I have appended the formula used in the solution part.

Q: Find the derivative of the function. 5 + 6x - 4/x y% =

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Q: Using the definition of derivative, find the derivative of f(x) = x² + 6x + 6. %3D

A: Using definition of derivatives.

Q: Find the derivative. y= 4x²e- x- y%3D4X

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Q: Find the derivative of the function. F(x) = (7x6 + 8x³)4 %3D

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