Differentiation of e^cotx | Differentiate e^cotx

The differentiation of e^cotx is equal to -cosec2x ecotx. In this post, we will learn how to differentiate e to the power cotx with respect to x.

Differentiation of e^cotx

The following two formulas will be used to find the derivative of ecotx.

  1. d/dx(cotx) = -cosec2x.
  2. loga ak =k.

Now, we will learn to find the derivative of e to the power cotx with respect to x.

How to Find the derivative of ecotx

Question: How to differentiate ecotx?


Let y= ecotx

Taking natural logarithms on both sides, we get that (natural logarithm means the logarithm with base e, i.e. loge)

log y = cotx

[Here we have used the above formula 2]

Now, differentiate both sides with respect to x. This will give us

$\dfrac{1}{y} \dfrac{dy}{dx}$ = -cosec2x, by the above formula 1.

⇒ $\dfrac{dy}{dx}$ = -y cosec2x

Now put back the value of y, that is, y=ecotx. Therefore, we obtain that

$\dfrac{d}{dx}$(ecotx) = – ecotx cosec2x.

Thus, the differentiation of ecotx with respect to x is equal to -ecotx cosec2x.


Derivative of arc(cotx): The derivative of arc(cotx) is -1/(1+x2).

Differentiate esinx: The derivative of esinx is esinx cosx.

Differentiate ecosx: The derivative of ecosx is -ecosx sinx.

Differentiate etanx: The derivative of etanx is etanx sec2x.


Q1: What is the derivative of ecotx?

Answer: The derivative of e^cotx is equal to -cosec2x ecotx.

Q2: If y=ecotx, then find dy/dx?

Answer: If y=ecotx, then dy/dx = -cosec2x ecotx.

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