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Popular >

derivative of-cos(x/2)

Solution

\frac{d}{d x} (- cos (\frac{x}{2}))

Solution

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

Solution steps

\frac{d}{d x} (- cos (\frac{x}{2}))

Take the constant out:

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

= - \frac{d}{d x} (cos (\frac{x}{2}))

Apply the chain rule:

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

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

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

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

Simplify

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

Popular Examples

tangent of (-6x)/((x^2+1))tangent of

\frac{- 6 x}{( x ^{2} + 1 )}

derivative of (sin^2(x)/(1+cos^2(x)))

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

integral of 1/((4x+5)^2)

\int \frac{1}{( 4 x + 5 ) ^{2}} d x

tangent of (8x)/((x+1)^2)tangent of

\frac{8 x}{( x + 1 ) ^{2}}

integral of 1/((y^2+1))

\int \frac{1}{( y ^{2} + 1 )} d y

Frequently Asked Questions (FAQ)

What is the derivative of-cos(x/2) ?
The derivative of-cos(x/2) is 1/2 sin(x/2)
What is the first derivative of-cos(x/2) ?
The first derivative of-cos(x/2) is 1/2 sin(x/2)