How do you find the derivative of $(cos x) (sin x)$ $(cosx)(sinx)$ ?

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How do you find the derivative of $(cos x) (sin x)$ $(cosx)(sinx)$ ?

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Answer 1 · 2016-07-17T05:36:41

Use the product rule:
$\frac{d}{d x} (cos x) \cdot sin x + \frac{d}{d x} (sin x) \cdot cos x$ $d/dx (cosx) *sinx +d/dx (sinx) *cosx$
$= - sin x \cdot sin x + cos x \cdot cos x$ $=-sinx *sinx +cosx *cosx$
$= {cos}^{2} x - {sin}^{2} x$ $=cos^2x-sin^2x$

The answer could also take the form $2 {cos}^{2} x - 1$ $2cos^2x -1$ arriving at this answer involves the use of trigonometric identities.

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How do you find the derivative of $(cos x) (sin x)$ $(cosx)(sinx)$ ?

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