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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

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

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