From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for the derivative g'(x) of g(x) = x´f(x) in terms of f(x) and f'(x).

Q: find the derivative  f(x)=x+3+4/x

A: The derivative of the function as follows.

Q: Give two applications of the derivative f(x + h) - f(x) f'(x) = lim h

A: The given function f'x=limh→0f(x+h)-f(x)h is the derivative by first principle.

Q: Find the derivative using the definition of the derivative for f(x) = Vx (ie. f'(x) = fn &+h)-{(x) ,…

A:

Q: Determine the derivative of the function L(x) In(2x) x² + 5

A: Given query is to find the derivative of the function.

Q: f(x)=πcos⁡(πx).  Find the twentieth derivative of f(x)

A: After third derivative, the sign will become positive because of the Cosine and the coefficient will…

Q: find the derivative  f(x)=x2(x3-1)

A: Apply the product rule and obtain the derivative of the given function.

Q: Find the derivative of f(x) = (5x ² - 8 x) 5 4 f(x) =

A: The objective of this question is to find the derivative of the function f(x) = (5x^2 - 8x)^5. This…

Q: Find the derivative of the function f(x) = /(x³+ 11x) by using the definition of the derivative.

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Q: find the derivative  f(x) = (x-1)3 (x- 1/x)4

A: