How do you differentiate $f (x) = {sin}^{2} x$ $f(x) = sin^2 x$ ?

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Answer 1 · 2017-03-01T16:03:48

$2 sin x \cdot cos x$ $2sinx*cosx$

It is helpful to write this function as
$f (x) = {(sin x)}^{2}$ $f(x)=(sinx)^2$ . Notice that both are equivalent.

Next differentiate using the chain rule.

Recall that the chain rule gives us a method to differentiate compositions. It is similar to the power but with an extra step

$d/(dx)f(g(x))=f'(g(x))*g'(x)$

For this function:
$f(x)=g(x)^2$ and $g(x)=sinx$

If:

$d/(dx)f(x)=2g(x)^1$ by the power rule

$d/(dx)sinx=cosx$ (memorize this)

Then:
$d/(dx)(sinx)^2$ $=2sinx*cosx$

How do you differentiate f(x) = sin^2 xf(x)=sin2x f(x) = sin^2 x?