What is the d/(dθ)(sin(θ/2)) ?

The d/(dθ)(sin(θ/2)) is cos(θ/2) 1/2

What is the first d/(dθ)(sin(θ/2)) ?

The first d/(dθ)(sin(θ/2)) is cos(θ/2) 1/2

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\frac{d}{d θ} (sin (\frac{θ}{2}))

cos (\frac{θ}{2}) \frac{1}{2}

Solution steps

\frac{d}{d θ} (sin (\frac{θ}{2}))

Apply the chain rule:

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

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

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

= cos (\frac{θ}{2}) \frac{1}{2}

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

\frac{d}{d x} (\frac{x ^{3} - 3 x ^{2} + 9}{x ^{2}})

\int (x - 2)^{5} d x

\frac{d}{d x} (12 x^{5} + 45 x^{4} - 200 x^{3} + 4)

y = x^{2} - 2, y = x