100. Use the derivative to help explain why g(x) = -2x – x³ decreases for all x in (-*, x).

Q: Find the Derivative f(x) = cosh(In(4x))

A:

Q: Find the derivative of: f(x) = (x3 + 2) In(x)

A: Consider the function

Q: 9. Use the definition of derivative to find the derivative of f(x) = x² – 3x.

A: We need to evaluate the derivative of the function f(x) using definition of the following function…

Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: What is the first derivative of g(x) = In 4x²+4x+8 ? x 3 tan x

A: we use Logarithmic properties

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

A:

Q: 1) Use the limit definition to find the derivative of the function f(x) = 3x – 5x?. Then find all…

A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

Q: 8. Find the derivative of f(x) = (1+x³)' ( 14x + - ) using differentiation rules.

A: topic - derivative of a function

Q: Which functions have a negative first derivative for all x?

A: Which functions have a negative first derivative for all x?

Q: Evaluate the 3rd derivative of y= x5Tan(x4) if x=4

A:

Q: 2. f(x) = x2– 5x + 6 at x 2 --

A:

Q: What is the derivative of the function with respect to x of (x + 1)³ – æ° -

A: Given : Function x+13 - x3   To find : Derivative of the given function with respect to x?

Q: how would you, using a limit def. of a derivative at a point find f'(-1) for the function f(x). =…

A: Hint:

Q: What is the first derivative of f(x) = ]n( 3x´+7x 5x

A:

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: Find the derivative f(x)= In(ex+9)

A: find the derivative

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: 16. Use the limit definition of the derivative to find the instantaneous rate of change for the…

A:

Q: Suppose 8 (x) =sec='(x<). what is the derivative of g with respect to x?

A: We can find the answer as below.

Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: Find the derivative of f(x) = 6* – 3* + In x -

A: Differentiate: fx=6x-3x+lnx

Q: 84. Use the definition of the derivative to directly prove thedifferentiation rules for constant and…

A: The definition of derivative states that: f'x=limh→0fx+h-fxh Let the function be fx=c, where c is a…

Q: Find the derivative of f (x) = -4 tan (x).

A:

Q: Use definition of derivative to find derivative of the function f(x)=3/x+2, at x=-1

A: Given f(x)=3x+2    at x=-1To find f'(x) at x=-1

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

A:

Q: Let f(x)=9−(4x^2+3x). Then according to the definition of derivative

A:

Q: Which of the following could be an anti-derivative of f(x)= x square root of x-2 end root?

A:

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: Find the derivative off (x) = 9x - 5 at x = 2 and x = 5.

A: Given f (x) = 9x - 5

Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Find the derivative of the function. f(x) = 4x In 4x f'(x)=

A:

Q: find the derivative by using the definition of a deriviative.f(x)= 1/3x+2

A: according to definition of derivative we will evaluate the derivative of f(x)

Q: Find the Do not include "f'(x) =" in your answer. derivative of f(x) = (-x³ - 2x² - 2x) sin (x).

A: Given f(x)=(-x3-2x2-2x)sin(x)

Q: Evaluate the derivative at the given value of x. 10) f(x) = x2 + 5x at x = 4 %3D

A: I did with limit definition of derivative

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

Q: 9. Use the definition of a derivative change of the functions below at f(x)% = x² + 2x

A:

Q: 10 Use the power rule to find the derivative of f(x) = Vx.

A: Given,          The function is fx=x10 .

Q: 1) Use the limit definition to find the derivative of the function f(x) = 6x – x². Then find all…

A: Using limits definition:f'(x) = limh→0 f(x+h) - f(x)hf(x) = 6x - x2f(x+h) = 6(x+h)- (x+h)2   = 6x +…

Q: 1 Use the limit definition of the derivative to find f'(x) if f (x)= 10x

A:

Q: Find the derivative. Simplify where possible. y  = x tanh-1 x   + In √ (1- x2)

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

Q: 13 Use the power rule to find the derivative of f(x) = 'Vx.

A:

Q: 2) Find the derivative of the function f(x) = 3x² by definition

A:

Q: 27. Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Derivative of the function f(x) is given by

Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

A:

Q: 7 Use the power rule to find the derivative of f(x) = x f'(x) =

A: Power Rule: The power for the derivative of the function xa is given by, The given function is f(x)…

Q: What is the 1881th derivative of the function given by f(x)=1881x + 1923 at the point x=2020.

A: