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Differentiate the following functions wi...

Differentiate the following functions with respect to `x` :
`sin 2x cos 3x`.

A

`(3 sin 2x sin 3x + 2 cos 3x cos 2x)`

B

`(-3 sin 2x sin 3x + 2 cos 3x cos 2x)`

C

`(-3 sin 2x sin 3x - 2 cos 3x cos 2x)`

D

`(3 sin 2x sin 3x - 2 cos 3x cos 2x)`

Text Solution

Verified by Experts

The correct Answer is:
B
By using the product rule, we have
`d/(dx) (sin 2x cos 3x) = (sin 2x). (d)/(dx) (cos 3x) + (cos 3x) . (d)/(dx) (sin 2x)`
`= (sin2x).(-sin3x).3+(cos3x).(cos2x).2` [using chain rule]
`= (-3 sin 2x sin 3x + 2 cos 3x cos 2x)` .
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