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Popular >

derivative of (sin^2(x)/4)

Solution

\frac{d}{d x} (\frac{sin ^{2} ( x )}{4})

Solution

\frac{sin ( 2 x )}{4}

Solution steps

\frac{d}{d x} (\frac{sin ^{2} ( x )}{4})

Take the constant out:

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

= \frac{1}{4} \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}{4} \cdot 2 sin (x) cos (x)

Simplify

\frac{1}{4} \cdot 2 sin (x) cos (x) : \frac{sin ( 2 x )}{4}

= \frac{sin ( 2 x )}{4}

Popular Examples

derivative of e^xln(x^2)

\frac{d}{d x} (e^{x} ln (x^{2}))

(dy)/(dx)=(xy)/(x^2+1)

\frac{d y}{d x} = \frac{x y}{x ^{2} + 1}

derivative of f(x)=-3x^2+24x-36 derivative of

f (x) = - 3 x^{2} + 24 x - 36

y^'=(2x)/(1+2y)

y^{^{'}} = \frac{2 x}{1 + 2 y}

tangent of f(x)=6sin(x),(pi/6 ,3)tangent of

f (x) = 6 sin (x), (\frac{π}{6}, 3)

Frequently Asked Questions (FAQ)

What is the derivative of (sin^2(x)/4) ?
The derivative of (sin^2(x)/4) is (sin(2x))/4
What is the first derivative of (sin^2(x)/4) ?
The first derivative of (sin^2(x)/4) is (sin(2x))/4