What is the derivative of sin(cos(3x)) ?

The derivative of sin(cos(3x)) is -3cos(cos(3x))sin(3x)

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

The first derivative of sin(cos(3x)) is -3cos(cos(3x))sin(3x)

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

- 3 cos (cos (3 x)) sin (3 x)

Solution steps

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

Apply the chain rule:

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

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

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

= cos (cos (3 x)) (- sin (3 x) \cdot 3)

Simplify

= - 3 cos (cos (3 x)) sin (3 x)

What is the derivative of sin(cos(3x)) ?
The derivative of sin(cos(3x)) is -3cos(cos(3x))sin(3x)
What is the first derivative of sin(cos(3x)) ?
The first derivative of sin(cos(3x)) is -3cos(cos(3x))sin(3x)