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Popular >

d/(dθ)(sin^2(θ/2))

Solution

\frac{d}{d θ} (sin^{2} (\frac{θ}{2}))

Solution

\frac{sin ( θ )}{2}

Solution steps

\frac{d}{d θ} (sin^{2} (\frac{θ}{2}))

Apply the chain rule:

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

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

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

= 2 sin (\frac{θ}{2}) cos (\frac{θ}{2}) \frac{1}{2}

Simplify

2 sin (\frac{θ}{2}) cos (\frac{θ}{2}) \frac{1}{2} : \frac{sin ( θ )}{2}

= \frac{sin ( θ )}{2}

Popular Examples

tangent of f(x)=x^2(2x+1/x),\at x=3 tangent of

f (x) = x^{2} (2 x + \frac{1}{x}), at x = 3

integral of 7x-sqrt(x)

\int 7 x - x d x

derivative of y=ln(-3x^6)derivative of

y = ln (- 3 x^{6})

(1+y^2)dx-(x^2+1)dy=0

(1 + y^{2}) d x - (x^{2} + 1) d y = 0

(\partial)/(\partial x)((-y^4)/(4x^4))

\frac{\partial}{\partial x} (\frac{- y ^{4}}{4 x ^{4}})

Frequently Asked Questions (FAQ)

What is the d/(dθ)(sin^2(θ/2)) ?
The d/(dθ)(sin^2(θ/2)) is (sin(θ))/2
What is the first d/(dθ)(sin^2(θ/2)) ?
The first d/(dθ)(sin^2(θ/2)) is (sin(θ))/2