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Basic Trigonometric Identities

Differentiate...

Question

Differentiate $s i n 2 x c o s 3 x .$

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Solution

By using the product rule, we have

$\frac{d}{d x} (s i n 2 x c o s 3 x) = (s i n 2 x) . \frac{d}{d x} . (c o s 3 x) + (c o s 3 x) . \frac{d}{d x} (s i n 2 x)$

$= (s i n 2 x) . (- s i n 3 x) .3 + (c o s 3 x) . (c o s 2 x) .2$ [using chain rule]

=-3~sin~2x~sin~3x~+2~cos~3x~cos~2x

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