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Differentiation Rules

Chain Rule


What is the derivative of y=4tan4x?y=4\tan^{4} x?

f(x)f(x) is a differentiable function such that f(2)=3f(2)=3 and f(2)=3.f'(2)=3. If g(x)=(x2f(x))2,g(x)=\left(x^2f(x)\right)^2, what is the value of g(2)?g'(2)?

What is the derivative of y=3x64?y=3 ^{x^ 6-4}?

Consider the function f(x)=log8[(3x1)3].f(x)=\log_{8} \left[ (3x-1)^3 \right] . What is the value of aa such that f(a)=9ln8?f'(a)=\frac{9}{\ln 8}?

If the instantaneous rate of change of y=sin1(3x)y=\sin^{-1} (3x) at x=16x=\frac{1}{6} can be expressed as 18a,\frac{18}{\sqrt{a}}, what is the value of a?a?


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