What is (\partial)/(\partial t)(sin^2(t)) ?

The answer to (\partial)/(\partial t)(sin^2(t)) is sin(2t)

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(\partial)/(\partial t)(sin^2(t))

\frac{\partial}{\partial t} (sin^{2} (t))

sin (2 t)

Solution steps

\frac{\partial}{\partial t} (sin^{2} (t))

Apply the chain rule:

2 sin (t) \frac{\partial}{\partial t} (sin (t))

= 2 sin (t) \frac{\partial}{\partial t} (sin (t))

\frac{\partial}{\partial t} (sin (t)) = cos (t)

= 2 sin (t) cos (t)

Use the Double Angle identity:

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

= sin (2 t)

\int 5 x + 1 d x

\frac{s}{( s ^{2} + 25 ) ^{2}}

\int 3 x (5 - x) d x

x \to 0 lim (\frac{x}{2 tan ( x )})

\frac{d}{d x} (\frac{x ^{3}}{6})

What is (\partial)/(\partial t)(sin^2(t)) ?
The answer to (\partial)/(\partial t)(sin^2(t)) is sin(2t)