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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.

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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