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

The d/(dt)(sin^2(t)) is sin(2t)

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

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

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

sin (2 t)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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)

\frac{d}{d x} (6 e^{x} + 2 y)

(2 x - 4) \frac{d y}{d x} - y^{2} = 0

\frac{d}{d x} (cos (x) cos (x))

\frac{d}{d x} (\frac{x + 8}{3 x ^{2} e ^{x}})

\frac{d}{d x} (- \frac{x ^{2}}{2} + 5 x + 3)