What is the derivative of sqrt(sin(4x)) ?

The derivative of sqrt(sin(4x)) is 2cos(4x)sqrt(csc(4x))

What is the first derivative of sqrt(sin(4x)) ?

The first derivative of sqrt(sin(4x)) is 2cos(4x)sqrt(csc(4x))

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

2 cos (4 x) csc (4 x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 2 cos (4 x) csc (4 x)

\frac{\partial}{\partial u} (u)

\frac{3 y ^{2}}{4 - 15 x y}

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

n = 0 \sum \infty \frac{( 2 ^{n + 1} )}{5 ^{n}}

What is the derivative of sqrt(sin(4x)) ?
The derivative of sqrt(sin(4x)) is 2cos(4x)sqrt(csc(4x))
What is the first derivative of sqrt(sin(4x)) ?
The first derivative of sqrt(sin(4x)) is 2cos(4x)sqrt(csc(4x))