Calculus

# Differentiation - Product Rule

If $f(x) = (x^2 - 10)(x^2 - 6 x + 2)$, what is the value of $f'(6)$?

If $f(x)=(x^2 - 3)(x^3-2x^2+5)$, what is $f'(1)$?

If $f(x) = (x+2) \sqrt{x-2}$, what is the value of $f'(27)$?

What is the derivative of $y=(\sin x)(7+5\cos x)?$

Given a function $A(x)$ such that \begin{aligned} A(x) & = f(x) \times g(x), \\ f(0)=g(0)&=4, {f}'(0) =7,{g}'(0)=8, \end{aligned} what is the value of ${A}'(0) ?$

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