What is the derivative of ${sin}^{3} x$ $sin^3x$ ?

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What is the derivative of ${sin}^{3} x$ $sin^3x$ ?

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Answer 1 · 2018-03-03T05:41:22

Basic formula:

$\frac{d}{d x} x^{n} = n x^{n - 1}$ $d/(dx)x^n=nx^(n-1)$

$\frac{d}{d x} (sin x) = cos x$ $d/dx(sinx)=cosx$

Now, let's move to the question:
$= \frac{d}{d x} ({sin}^{3} x)$ $color(white)=d/dx(sin^3x)$
$= (3 {sin}^{2} x) \times (\frac{d}{d x} (sin x))$ $=(3sin^2x)×(d/dx(sinx))$
$= 3 {sin}^{2} x cos x$ $=3sin^2xcosx$

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