What is the derivative of e^{cot(4x)} ?

The derivative of e^{cot(4x)} is -4e^{cot(4x)}csc^2(4x)

What is the first derivative of e^{cot(4x)} ?

The first derivative of e^{cot(4x)} is -4e^{cot(4x)}csc^2(4x)

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derivative of

e^{c o t (4 x)}

- 4 e^{c o t (4 x)} csc^{2} (4 x)

Solution steps

\frac{d}{d x} (e^{c o t (4 x)})

Apply the chain rule:

e^{c o t (4 x)} \frac{d}{d x} (cot (4 x))

= e^{c o t (4 x)} \frac{d}{d x} (cot (4 x))

\frac{d}{d x} (cot (4 x)) = - csc^{2} (4 x) \cdot 4

= e^{c o t (4 x)} (- csc^{2} (4 x) \cdot 4)

Simplify

= - 4 e^{c o t (4 x)} csc^{2} (4 x)

What is the derivative of e^{cot(4x)} ?
The derivative of e^{cot(4x)} is -4e^{cot(4x)}csc^2(4x)
What is the first derivative of e^{cot(4x)} ?
The first derivative of e^{cot(4x)} is -4e^{cot(4x)}csc^2(4x)