What is the derivative of e^{cos(3x)} ?

The derivative of e^{cos(3x)} is -3e^{cos(3x)}sin(3x)

What is the first derivative of e^{cos(3x)} ?

The first derivative of e^{cos(3x)} is -3e^{cos(3x)}sin(3x)

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derivative of

e^{c o s (3 x)}

- 3 e^{c o s (3 x)} sin (3 x)

Solution steps

\frac{d}{d x} (e^{c o s (3 x)})

Apply the chain rule:

e^{c o s (3 x)} \frac{d}{d x} (cos (3 x))

= e^{c o s (3 x)} \frac{d}{d x} (cos (3 x))

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

= e^{c o s (3 x)} (- sin (3 x) \cdot 3)

Simplify

= - 3 e^{c o s (3 x)} sin (3 x)

What is the derivative of e^{cos(3x)} ?
The derivative of e^{cos(3x)} is -3e^{cos(3x)}sin(3x)
What is the first derivative of e^{cos(3x)} ?
The first derivative of e^{cos(3x)} is -3e^{cos(3x)}sin(3x)