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Find derivative of function f(x)=sinx/sinx-cosx with …

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Find derivative of function f(x)=sinx/sinx-cosx with respect to x.

  • 1 answers

Naveen Sharma 8 years, 9 months ago

Ans. {tex}f(x) = {sinx\over sinx-cosx}{/tex}

Using quotient Rule, we get

{tex}f'(x) ={ {(sinx-cosx){d(sinx)\over dx}- sinx{d(sinx-cosx)\over dx}}\over (sinx-cosx)^2}{/tex}

{tex}=> { (sinx-cosx)cosx - sinx(cosx-(-sinx)) \over (sinx-cosx)^2}{/tex}

{tex}=> {sinx cosx - cos^2x -sinxcosx -sin^2x\over (sinx-cosx)^2}{/tex}

{tex}=> {- (cos^2x +sin^2x)\over (sinx-cosx)^2}{/tex}

{tex}=> {-1\over (sinx-cosx)^2}{/tex}

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