What is the derivative of e^{sin^2(x}) ?

The derivative of e^{sin^2(x}) is e^{sin^2(x)}sin(2x)

What is the first derivative of e^{sin^2(x}) ?

The first derivative of e^{sin^2(x}) is e^{sin^2(x)}sin(2x)

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\frac{d}{d x} (e^{s i n^{2} (x)})

e^{s i n^{2} (x)} sin (2 x)

Solution steps

\frac{d}{d x} (e^{s i n^{2} (x)})

Apply the chain rule:

e^{s i n^{2} (x)} \frac{d}{d x} (sin^{2} (x))

= e^{s i n^{2} (x)} \frac{d}{d x} (sin^{2} (x))

\frac{d}{d x} (sin^{2} (x)) = sin (2 x)

= e^{s i n^{2} (x)} sin (2 x)

What is the derivative of e^{sin^2(x}) ?
The derivative of e^{sin^2(x}) is e^{sin^2(x)}sin(2x)
What is the first derivative of e^{sin^2(x}) ?
The first derivative of e^{sin^2(x}) is e^{sin^2(x)}sin(2x)