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Continuity And Differentiability

Question

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Differentiate w.r.t.x: $cos left parenthesis square root of straight x right parenthesis$

Solution

Let space space space space space space space space space space space space space space space space space space space space space space space space straight y equals space cos left parenthesis square root of straight x right parenthesis therefore space space space space space space space space space space space space space space space space space space space space dy over dx equals straight d over dx open square brackets cos left parenthesis square root of straight x right parenthesis close square brackets equals negative sin left parenthesis square root of straight x right parenthesis. straight d over dx open parentheses straight x to the power of 1 half end exponent close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals negative sin left parenthesis square root of straight x right parenthesis.1 half straight x to the power of negative 1 half end exponent therefore space straight d over dx open square brackets cos left parenthesis square root of straight x right parenthesis close square brackets equals negative fraction numerator 1 over denominator 2 square root of straight x end fraction. sin square root of straight x

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