What is the derivative of sqrt(cos(xsin(x))) ?

The derivative of sqrt(cos(xsin(x))) is (cos(2x))/(2sqrt(cos(x)sin(x)))

What is the first derivative of sqrt(cos(xsin(x))) ?

The first derivative of sqrt(cos(xsin(x))) is (cos(2x))/(2sqrt(cos(x)sin(x)))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int tanh (2 x) d x

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

f (x) = \frac{x ^{2}}{100}

\frac{3}{( s + 4 ) ( s + 8 ) ^{2}}

\int (cos (5 x)) d x

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