d/dx [ sin(f(x)) ]
cos(f(x))*f'(x)
Using the chain rule, the derivative of sin(f(x)) with respect to x can be found as follows:
d/dx [ sin(f(x)) ] = cos(f(x)) * d/dx [ f(x) ]
This is because the derivative of the outer function, sin(x), is cos(x), and the derivative of the inner function, f(x), is d/dx [ f(x) ].
However, we may further simplify the expression using the chain rule on the inside:
d/dx [ sin(f(x)) ] = cos(f(x)) * d/dx [ f(x) ]
= cos(f(x)) * f'(x)
Therefore, the derivative of sin(f(x)) with respect to x is cos(f(x)) times the derivative of f(x).
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