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Question

Find the derivative oftan-1x(1+tan-1x) with respect to tan-1x.


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Solution

Find the required derivative.

Given function : tan-1x(1+tan-1x)

The derivative of tan-1x(1+tan-1x) with respect to tan-1x is

ddtanx-1xtan-1x(1+tan-1x)=1×(1+tan-1x)-tan-1x×1(1+tan-1x)2f'(x)=u'(x)×v(x)u(x)×v'(x)v(x)2=1+tan-1x-tan-1x(1+tan-1x)2=1(1+tan-1x)2

Hence, the derivative oftan-1x(1+tan-1x) with respect to tan-1x is 1(1+tan-1x)2.


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