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Popular >

derivative of 1/4 sin^2(2x)

Solution

\frac{d}{d x} (\frac{1}{4} sin^{2} (2 x))

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{4} sin^{2} (2 x))

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (sin^{2} (2 x))

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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

\frac{d y}{d x} = \frac{( y ^{2} + 2 x y )}{x ^{2}}

sum from n=1 to infinity of 3e^{-5n}

n = 1 \sum \infty 3 e^{- 5 n}

tangent of f(x)=9+4x^2-2x^3,\at x=2 tangent of

f (x) = 9 + 4 x^{2} - 2 x^{3}, at x = 2

tangent of f(x)=1+sqrt(4+x^2),\at x=0 tangent of

f (x) = 1 + 4 + x^{2}, at x = 0

f (x) = 8 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of 1/4 sin^2(2x) ?
The derivative of 1/4 sin^2(2x) is (sin(4x))/2
What is the first derivative of 1/4 sin^2(2x) ?
The first derivative of 1/4 sin^2(2x) is (sin(4x))/2