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  • Differentiate the functions with respect to x in sin ax + b

3. Differentiate the functions with respect to x in 

\sin (ax +b )

Answers (1)

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Given function is
f(x) = \sin (ax +b )
when we differentiate it w.r.t. x.
Lets take t = ax+b . then,
f(t) = \sin t
\frac{df(t)}{dx} = \frac{df(t)}{dt}.\frac{dt}{dx}                                          (By  chain rule)
\frac{df(t)}{dt} = \frac{d(\sin t )}{dt} = \cos t = \cos (ax+b)
\frac{dt}{dx} = \frac{d(ax+b )}{dx} = a
Now,
\frac{df(t)}{dx} = \frac{df(t)}{dt}.\frac{dt}{dx} = \cos (ax+b).a
Therefore, the answer is a \cos (ax+b)

Posted by

Gautam harsolia

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