Prove that the function ax+b f(x)= cx+d is constant (takes the same value for every x such that cx+d ‡0) if and only if a b=0. (Hint: Find the derivative of ƒ(x).)

Q: Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables…

A: Solution 2: Given function is f(x)=x14+x1x2+(1+x2)2           (1) Now, partially differentiating (1)…

Q: Find the derivatives of the following function f(x) from the first principles x4+4

A: Form first principal of derivative, use the limit as given below and find the derivative.

Q: Please answer and show all work thank you!!

A: ## To find a derivative , the equation must only be defined as a function of x , we want to find the…

Q: 11) find the derivative of the function.

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Q: Complete detailed solution. What is the derivative of 6 f(x)=(√2-1)(3√x+1)

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Q: Find the relative extrema of the following function. You may use either derivative test to figure…

A: The given function is: f(x)=-x4-8x3+32x2

Q: derivative

A: Please refer to the image below

Q: Question 6 You do not need to simplify the answer. :) For each of the following, use the quotient…

A: Given,  f(x)= (x2+x)x-2 = (x2+x)/x2 = (1+1/x) differentiate with respect to X, f'(x)= d/dx 1 + d/dx…

Q: (b) g(x):= 1/x for x E R, x#0, (d) k(x):= 1//x for x > 0.

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Q: Explain how f(x) = |x| is an example of a function that is continuous everywhere, but its derivative…

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Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

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Q: 2x + 1 2. g(x) = %3D 2x2 – x +1 |

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function (The…

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Q: Find the derivative of y with respect to the appropriate variable. y=cosh ¹2√√x+10 O A. B. O C. O D.…

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