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Popular >

derivative of (sin^2(x)/2)

Solution

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

Solution

sin (x) cos (x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= sin (x) cos (x)

Popular Examples

slope derivative of 5/(4x)-7/4 slope

\frac{d}{d x} (\frac{5}{4 x}) - \frac{7}{4}

integral of ((arctan(x))^3)/(1+x^2)

\int \frac{( arctan ( x ) ) ^{3}}{1 + x ^{2}} d x

(\partial)/(\partial x)(x/(x^2+(y-1)^2))

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + ( y - 1 ) ^{2}})

integral of 1/(12x)

\int \frac{1}{12 x} d x

derivative of log_{5}(x^2-7x)

\frac{d}{d x} (lo g_{5} (x^{2} - 7 x))

Frequently Asked Questions (FAQ)

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