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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Use the Double Angle identity:

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

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

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{2} + 1})

\frac{d}{d x} ((6 x + 5)^{x})

\int - \frac{2}{64 - 100 x ^{2}} d x

n = 0 \sum \infty \frac{x ^{n}}{2 n !}

(2.9) (- 3.2)

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