Question: EXAMPLE 2 Differentiate (a)y = sin(x7)and (b)sin7(x).SOLUTION(a) Ify = sin(x7),then the outer function is the sine function and the inner function is the power function,

EXAMPLE 2 Differentiate (a)y = sin(x7)and (b)sin7(x).SOLUTION(a) Ify = sin(x7),then the outer function is the sine function and the inner function is the power function, so the Chain Rule givesdydx=ddxsin(x7)=cos(x7)outerevaluatedderivativeevaluatedderivativefunctionat innerof outerat innerof innerfunctionfunctionfunctionfunction=.(b) Note thatsin7(x)=(sin(x)).Here the outer function is the power function and the inner function is the sine function. Sodydx=ddx(sin(x))7=7(sin(x))6innerderivative of outerderivativefunctionfunction evaluatedof innerat inner functionfunction

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