What is the derivative of 4cos(sin(3x)) ?

The derivative of 4cos(sin(3x)) is -12sin(sin(3x))cos(3x)

What is the first derivative of 4cos(sin(3x)) ?

The first derivative of 4cos(sin(3x)) is -12sin(sin(3x))cos(3x)

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\frac{d}{d x} (4 cos (sin (3 x)))

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

Solution steps

\frac{d}{d x} (4 cos (sin (3 x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (cos (sin (3 x)))

Apply the chain rule:

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

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

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

= 4 (- sin (sin (3 x)) cos (3 x) \cdot 3)

Simplify

= - 12 sin (sin (3 x)) cos (3 x)

What is the derivative of 4cos(sin(3x)) ?
The derivative of 4cos(sin(3x)) is -12sin(sin(3x))cos(3x)
What is the first derivative of 4cos(sin(3x)) ?
The first derivative of 4cos(sin(3x)) is -12sin(sin(3x))cos(3x)