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

The d/(dt)(sin(t/2)) is cos(t/2) 1/2

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

The first d/(dt)(sin(t/2)) is cos(t/2) 1/2

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

cos (\frac{t}{2}) \frac{1}{2}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d t} (\frac{t}{2}) = \frac{1}{2}

= cos (\frac{t}{2}) \frac{1}{2}

y^{^{'}} = 5

\int e^{\frac{3}{2} x} d x

t \frac{d y}{d t} + y = t^{2}

\int \frac{t}{t ^{2} + 1} d t

n = 1 \sum \infty (n + 1) x^{n}