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

Q: y= In(In.x)

A: t differentiate wrt x

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A: We have to use definition of differentiable:

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A: Given function is fx=x3+3x2+9. We know that, f'x=limx→cfx-fcx-c Given c=-3 Therefore,…

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

A: Given: f(y)=15y3lny

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

A:

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: Find the derivative of function.

A:

Q: Find the derivative of the function f. f(x) = e¯X tan(4x) %3D f'(x) = %3D

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Q: Define the derivative f'(a) of a function f at x =a.

A: To define: The derivative f'(a) of a function f(x) at x=a

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Q: Find the derivative of f(x) = x² cos r.

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A: Consider the function  f(x)=ec+cx,       c>0

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) =

A:

Q: Let y = f(x) = x² +1, evaluate the derivative of the inverse function x = f-l(y) at y = 2.

A: Given a function, y=f(x)=x2+1 To find the derivative of the inverse function of f(x).

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A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

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

A:

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: 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: Let y" = e* (g(x)) be the second derivative of y = Determine the value of g(X) if X= -4. (Use three…

A:

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: Find the derivative of function.

A: Use the product rule to find the derivative for s. s=t2lntdsdt=ddtt2×lnt+t2×ddtlnt

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

A: Given f(x)=x2-2 c=5

Q: Determine the derivative of y with respect to x: In x+ In y = x cos y

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Q: Let y be a function of x and suppose y=In(x²+y²). What is the correct result for the derivative of y…

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: Evaluate the derivative of the function y = 2tan ",²+In (e +e).

A:

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

A:

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

A:

Q: Find the derivative of y with respect to x. -1 y = tan (In(2x))

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

A:

Q: Determine the derivative of the following functions. 1. y = 9x cos(2x + 3) 2. y = cos(x + y)

A: According to the question, we need to calculate the derivative of the given function.    Function 1:…

Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

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

A:

Q: The 60th derivative of x with respect to y of y = x^60 is 60!x

A:

Q: Find the derivative of the function. y = a° + cos (x) y'(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

A:

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

A:

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 y" = e*(g(x)) be the second derivative of y = Determine the value of g(x) if x = -4. (Use three…

A:

Q: Find the derivative of y = f(x) = x cos(x).

A: y =f(x) = x cos xf'(x)=ddx (x cos x)

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

A: The alternate form refers here the definition of derivative.