What is the derivative of cos(3cos(2sqrt(x))) ?

The derivative of cos(3cos(2sqrt(x))) is (3sin(2sqrt(x))sin(3cos(2sqrt(x))))/(sqrt(x))

What is the first derivative of cos(3cos(2sqrt(x))) ?

The first derivative of cos(3cos(2sqrt(x))) is (3sin(2sqrt(x))sin(3cos(2sqrt(x))))/(sqrt(x))

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\frac{d}{d x} (cos (3 cos (2 x)))

\frac{3 sin ( 2 x ) sin ( 3 cos ( 2 x ) )}{x}

Solution steps

\frac{d}{d x} (cos (3 cos (2 x)))

Apply the chain rule:

- sin (3 cos (2 x)) \frac{d}{d x} (3 cos (2 x))

= - sin (3 cos (2 x)) \frac{d}{d x} (3 cos (2 x))

\frac{d}{d x} (3 cos (2 x)) = - \frac{3 sin ( 2 x )}{x}

= - sin (3 cos (2 x)) (- \frac{3 sin ( 2 x )}{x})

Simplify

- sin (3 cos (2 x)) (- \frac{3 sin ( 2 x )}{x}) : \frac{3 sin ( 2 x ) sin ( 3 cos ( 2 x ) )}{x}

= \frac{3 sin ( 2 x ) sin ( 3 cos ( 2 x ) )}{x}

e^{- 2 s}

f^{^{'}} (x) = - \frac{1}{x} (f (x))

\frac{s + 1}{s ^{2} + 2 s + 2}

\int \frac{1}{x} - 1 d x

\int (1 - cos^{2} (x)) sin (x) d x

What is the derivative of cos(3cos(2sqrt(x))) ?
The derivative of cos(3cos(2sqrt(x))) is (3sin(2sqrt(x))sin(3cos(2sqrt(x))))/(sqrt(x))
What is the first derivative of cos(3cos(2sqrt(x))) ?
The first derivative of cos(3cos(2sqrt(x))) is (3sin(2sqrt(x))sin(3cos(2sqrt(x))))/(sqrt(x))