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

Answer 1

The answer is #y=2sinxcosx=sin2x#

This function can be written as #f(x)=g(h(x))# where #g(x)=x^2# and #h(x)=sinx#. The derivative of such function has to be calculated as #[g(h(x))]'=g'[h(x)]*h'(x)# #[g(h(x))]'=2sinx*cosx# Now you can apply the double angle formula to write the answer as #y=sin2x#

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Answer 2

Evelyn Agard

To find the derivative of ( f(x) = \sin^2 x ), you can use the chain rule. First, differentiate the outer function (\sin^2 x) with respect to its inner function (\sin x), which is (2\sin x). Then, differentiate the inner function (\sin x) with respect to (x), which is (\cos x). Multiply these derivatives together to get the final result: (f'(x) = 2\sin x \cos x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.