Question

Differentiate 5^{log sin x} w.r.t.x.

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Solution

Let space space space space space straight y equals 5 to the power of log space sin space straight x end exponent therefore space dy over dx equals 5 to the power of log space sin space straight x end exponent. log 5. straight d over dx left parenthesis log space sin space straight x right parenthesis equals 5 to the power of log space sin space straight x end exponent. log 5. fraction numerator 1 over denominator sin space straight x end fraction. straight d over dx left parenthesis sin space straight x right parenthesis space space space space space space space space space space space space space equals 5 to the power of log space sin space straight x end exponent. log 5. fraction numerator 1 over denominator sin space straight x end fraction. cos space straight x equals cot. log 5.5 to the power of log space sin space straight x end exponent

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