What is the d/(dt)(sin^2(e^{sin^2(t)})) ?

The d/(dt)(sin^2(e^{sin^2(t)})) is e^{sin^2(t)}sin(2e^{sin^2(t)})sin(2t)

What is the first d/(dt)(sin^2(e^{sin^2(t)})) ?

The first d/(dt)(sin^2(e^{sin^2(t)})) is e^{sin^2(t)}sin(2e^{sin^2(t)})sin(2t)

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\frac{d}{d t} (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{\partial}{\partial z} (\frac{z ^{2}}{y})

\frac{d}{d x} (x^{2} - cos (2 x))

(12 + x^{2}) y^{^{'}} - 2 x y = 0

x \to 0 + lim (x^{x})

\frac{\partial}{\partial x} (x^{6} - 8 x^{3} y)

What is the d/(dt)(sin^2(e^{sin^2(t)})) ?
The d/(dt)(sin^2(e^{sin^2(t)})) is e^{sin^2(t)}sin(2e^{sin^2(t)})sin(2t)
What is the first d/(dt)(sin^2(e^{sin^2(t)})) ?
The first d/(dt)(sin^2(e^{sin^2(t)})) is e^{sin^2(t)}sin(2e^{sin^2(t)})sin(2t)