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Differentiation Rules

Applying Differentiation Rules to Trigonometric Functions


If the derivative of y=sin1(x24)y=\sin^{-1} (x^2-4) can be expressed as 2xf(x),\frac{2x}{\sqrt{f(x)}}, what is f(x)?f(x)?

If the instantaneous rate of change of y=tan1x1x+1y=\tan^{-1} \frac{x-1}{x+1} at x=23x=23 is a,a, what is the value of 1a?\frac{1}{a}?

If 2x=sin11922082x = \sin^{-1} \frac{192}{208}, the rate of change of y=sinxcosx y = \sin x \cos x can be expressed as ab\frac{a}{b}, where aa and bb are coprime integers. What is a+ba+b?

If the derivative of y=cos1(66x)y=\cos^{-1} (6-6x) can be expressed as 6f(x),\frac{6}{\sqrt{f(x)}}, what is f(x)?f(x)?

What is the derivative of y=3sin4x?y=3\sin^{4} x?


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