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

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

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

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

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derivative of

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

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

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

Use the Double Angle identity:

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

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

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