Question

Differentiate sin^-1(e^x) w.r.t.x.

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Solution

Let space space space space space straight y equals sin to the power of negative 1 end exponent left parenthesis straight e to the power of straight x right parenthesis therefore space dy over dx equals fraction numerator 1 over denominator square root of 1 minus left parenthesis straight e to the power of straight x right parenthesis end root end fraction straight d over dx left parenthesis straight e to the power of straight x right parenthesis equals fraction numerator 1 over denominator square root of 1 minus straight e to the power of 2 straight x end exponent end root end fraction. straight e to the power of straight x equals fraction numerator straight e to the power of straight x over denominator square root of 1 minus straight e to the power of 2 straight x end exponent end root end fraction

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