Apply the sum and difference rules to combine derivatives Question Let h(x) = f(x) +g(x). If f(x) = 6x and g(x) = 3x², what is h'(-1)? %3D Do not include "h (-1) =" in your answer. For example, if you found h'(-1) = 7, you would enter 7. Provide your answer below: MacBook Pro

Q: y = In (x* + 5)³

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Q: How to find the derivative of d/dx [(x^2-6)(2x^2+5x)]

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Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: A second derivative Findd2y/dx2 if x2 + y2 = 1.

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Q: Find the derivative of the given function at a given number. 1. y = 3x² - 2 at f'(1)

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Q: 1) Find the derivative of y =-+x-1 %3D

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Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: Determine Step 3 using 4-Step Rule in finding the derivative of  y=2sin(x)cos(x).

A: Introduction: The four-step method to find derivatives is actually determining the derivative of a…

Q: Find the derivatives of x^ x (x>0) with respect to x, find first principles

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Q: Find the derivatives of the functions in Exercis y = (1 + 2x)e-2x

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Q: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

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Q: Find the first derivative of f(x) = e3r

A: To find the first derivative of fx=x3e3x. Solution: Quotient rule of derivative states that:…

Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: 4. Find the 2nd derivative of f(x)=14-x (x)%3D

A: The give function is fx=4-x

Q: Shows the derivative function of: e3x+5

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Q: find implicit derivative of x^3 + x tan^-1 y = e^y

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Q: d100 y (100th derivatives) dx100 b.y = x100 ; find

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Q: 2х Find the second orfer derivatives of y=Tan" 1-x3

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Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

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Q: 7.) f (x)> (3x+2)(5x-2)

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Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: 6 Find the derivative of f (y) =7tan(y) - 6.

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Q: 1 14) Use the definition of derivative to find dx 3- х.

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Q: The second derivative of a function is equal to 1. If the graph of the function passes through (0,2)…

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Q: 1. y=ex-4) (exponent of (x-4) is 2) %3D

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Q: Example 2: by using the definition of the derivative, find dy/dx of the function y = 5x + 8x - 3x +4

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Q: a.) z= 5.

A: We will find the second derivative of the given function in the following step.

Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

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Q: (# 11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f (x) =…

A: For the equation of tangent, we need to find the slope of the function at x=1.

Q: Example 2: by using the definition of the derivative, find dy/dx of the function y 5x' + 8x - 3x +4

A: We can use definition of limit In order to solve the given problem.

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: 3. Find the derivative of f(x). (a) f(x) = e cos x (b) f(x) = (2x³ 4x-¹) cotx -

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Q: 2x By applying the derivatives from first principle, find the derivatives of y = 5х.

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Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x %3D

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Q: k(x) = x In x %3D

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Q: 1) Find the second derivative of f (x) = 24 . %3D

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Q: the Chain Rule.

A: Given: y=11-x46. Let, u=1-x4 By chain rule, the derivative of y with respect to x is given as,…

Q: Find the derivative of -3x f(x) = e¯* + e2x - e %3D

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Q: Find the derivative of the function. h(x) ető - x + 1 ets

A: hx=ex8-x+1

Q: 10 The derivative of f(x)= - is

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Q: 5x f(X) = V2x+3 %3D Find the first derivative given that

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Q: Find the derivative of the function. y = etan(8) y' =

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Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: 2) Use the chain rule. (Chapter 2.5) Find the derivative y= (x² +3x)*

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Q: 31. Using one-sided derivatives, show that the function f(x) = {2. [x² +x, | 3х — 2, х> 1 does not…

A: Given: fx=x2+x     , x≤13x-2   ,  x>1

Q: 8ubject find the derivative of y= X. Ln (esé'sx)

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Q: 1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

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