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

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

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

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

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العربية

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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