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Popular >

derivative of sqrt(sin(xcos(x)))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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limit as x approaches 1 of (x-1)^{(x-1)}

x \to 1 lim ((x - 1)^{(x - 1)})

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\int_{0}^{x} 10 cos (x + y + z) d z

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\frac{\partial}{\partial x} (x^{4} y^{2} + 4 y^{4} - x^{3})

integral of 5cos^4(x)

\int 5 cos^{4} (x) d x

Frequently Asked Questions (FAQ)

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