Let y be a function of x and suppose y=In(x²+y²). What is the correct result for the derivative of y with respect to x?

Q: y= In(In.x)

A: t differentiate wrt x

Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: Give the derivative formula for the function. j(x) 4 In x e5 = j(x)

A: The function is given by,

Q: Find the derivative of the function.

A:

Q: Let z = a + ib and f(x) = exp (zæ), then find the 1st and 2nd derivative of f(x).

A: Given: f(x)=ezxwhere,z=a+ib

Q: Use the alternative form of the derivative to find the derivative at x=c ( if it exists). f(x) =…

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Q: Find the derivative of the function. A y = 7tan-(x - V1 + x²) %3D (2* * I^ -

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 11) y = In 1-x (x +4)3

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Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = ∣x…

A: Concept: Derivative is the amount by which function is changing at one point. Given:

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). f(x) = x2…

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Q: Find the derivative of f (y) = 153/g In(y)

A: Given: f(y)=15y3lny

Q: Compute the derivative of the following function. 1(x) = 3e 3x f'X)%3D

A: Topic - differentiation

Q: Use the alternative form of the derivative to find the derivative at x = c  (if it exists). f(x) =…

A: Definition used -           Alternative form of derivative -…

Q: Let y=x+∣∣x2−8∣∣. Find the derivative of the function at x=3.

A: Given that y=x+x2-8.

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = 2x2…

A: Given function is gx=2x2-3x. We know that, f'x=limx→cfx-fcx-c Using the above formula of derivative,…

Q: Find the derivative of the function f(x) = x2 - 5x + 3 at the numbers (a) 2 and (b) a. %3D

A: a. From the definition we have the following, Simplify further,

Q: Use the alternate form of the derivative to find the derivative at x=c, if it exists. f(x) = x³ +…

A: Given f(x) = x³ + 2x² + 1, c = -2 Find the derivative at x= c if exist by using the alternate form…

Q: Find the derivative of the function. r(x) = In(x + 1) + 5x7ex r'(x) =

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: Let f (x) =e*. cos(x²).what is the correct result of the derivative of f

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Q: Use the rules for derivatives to find the derivative of function defined as follows.

A: The given function is: y=ln2x-1x+3 To find the derivative of this function, apply the quotient rule,…

Q: Use the definition of the derivative to show that the derivative of y = f(x)3 2/ is 1 f'(z) = VI %3D

A: GIVEN f(x) = 2√ x CALCULATE f'(x) = 1/ √ x

Q: Find the derivative of a linear function y=ax+b using the definition of derivative.

A: The derivative of a function f' of function f is defined as f'x=limh→0fx+h-fhh

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y 2xe X- 2e X O 2xeX O 2xeX +…

A: Finding the derivative

Q: Compute the derivative function f'(x) algebraically. f(x) = 8x – 5 %3D f'(x) =

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists .

A:

Q: Find the derivative of y with respect to x.

A:

Q: Give two different interpretations of the derivative of the function y = f(x) at x = a.

A: If f(x) represents a quantity at any x then the derivative f′(a) represents the instantaneous rate…

Q: Find the derivative of the function y(x) = n² +r". Assume that n is a positive y(x) = | constant.

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Find the derivative of y with respect to x if y = (12x - 24x + 24) e - 3x. y' =D %3D

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find the derivative of the function. y = cos(a + x*) У (x) %3

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Q: Find the derivative of the function y=(x−1)(x−2)(x−3) at x=0.

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Q: 2. (x² – y²)³ = 3a*x? %3D

A: The given equation is x2-y23=3a4x2 We have to find the derivative of y with respect to x. In this…

Q: Find the derivative of y with respect to x in the following functions: y= Ju +2u and u x2-3

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Q: Ax) = Vã Vx = /x хх e

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: Find the derivative of y with respect to x. x7 x7 X' Inx- 98 y = 14

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

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Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = (x…

A: Given function is fx=x-623. To find the derivaitve of the function at x=c. Differentiating with…

Q: find the derivative of the following function x2y= (y+2) + xysin(x)

A:

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = x2…

A: Solution:-  The given function is  g(x)=x2-xwe have to use alternative form of derivative to find…

Q: Find the derivative of the following function. ° 4x y = In x y' =O %3D

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Q: acos(b/x f(x) 2 (x^q)s

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Q: Obtain the derivative of the function f(x) = 6cos(2x) TC and find the value of this derivative when…

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Q: Find the derivative of g(x) = J2x u²+1

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Q: Suppose =V1+ Vx. What is the correct result of the derivative of g with respect to x? A 8'(x) = 2/1+…

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Q: Give the derivative formula for the function. (x)2 In x -e j'(x)

A: Consider the given function.

Q: Find the derivative.

A: Given,

Q: Let f(x) = 3x² + 2x − 10; a = 1. 1. Use the definition to find the derivative function f' 2. Find an…

A: The given function is: f(x)=3x2+2x-10

Q: The derivative of a^u with respect to x is

A: Aim:- To calculate : ddx(au)