How do you find the derivative for #k(x) = sin (x^2+2)#?

1 Answer
KillerBunny
Apr 6, 2015

Using the chain rule, which states that the derivative of #f(g(x))# is #f'(g(x)) * g'(x)#. In your case, the outer function #f(x)# is #\sin(x)#, and the inner function #g(x)# is #x^2+2#.

This means that #f'(x)=\cos(x)#, and #g'(x)=2x#.

Plugging these results into the chain rule formula, we get

#d/dx sin(x^2+2)= \cos(x^2+2) * 2x#

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