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# Differentiation Rules

These are the rules that explain how to take derivatives of any functions: from polynomials to trigonometric functions to logarithms.

# 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{align} A(x) & = f(x) \times g(x), \\ f(0)=g(0)&=4, {f}'(0) =7,{g}'(0)=8, \end{align} what is the value of $${A}'(0) ?$$

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