Differentiation Rules

Differentiation - Product Rule


If f(x)=(x210)(x26x+2) f(x) = (x^2 - 10)(x^2 - 6 x + 2) , what is the value of f(6) f'(6) ?

If f(x)=(x23)(x32x2+5)f(x)=(x^2 - 3)(x^3-2x^2+5), what is f(1)f'(1)?

If f(x)=(x+2)x2 f(x) = (x+2) \sqrt{x-2} , what is the value of f(27) f'(27) ?

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

Given a function A(x)A(x) such that A(x)=f(x)×g(x),f(0)=g(0)=4,f(0)=7,g(0)=8,\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)? {A}'(0) ?


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