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Popular >

derivative of sin^2(x/2)

Solution

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

Solution

\frac{sin ( x )}{2}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{sin ( x )}{2}

Popular Examples

derivative of ln(7x^2+5y^2)

\frac{d}{d x} (ln (7 x^{2} + 5 y^{2}))

derivative of 4t^{(-1)/8}+5ln(t)+ln(5)derivative of

4 t^{\frac{- 1}{8}} + 5 ln (t) + ln (5)

sum from n=1 to infinity of 3/(5^n)+2/n

n = 1 \sum \infty \frac{3}{5 ^{n}} + \frac{2}{n}

tangent of f(x)=3x^2-4x+1 tangent of

f (x) = 3 x^{2} - 4 x + 1

area y=4,y=x^2 area

y = 4, y = x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of sin^2(x/2) ?
The derivative of sin^2(x/2) is (sin(x))/2
What is the first derivative of sin^2(x/2) ?
The first derivative of sin^2(x/2) is (sin(x))/2