Differentiation of e^tanx | Differentiate e^tanx

The differentiation of e^tanx is equal to sec2x etanx. In this post, we will learn how to differentiate e to the power tanx with respect to x.

Differentiation of e^tanx

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

  1. d/dx(tanx) = sec2x.
  2. loga ak =k.

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

How to Find the derivative of etanx

Question: How to differentiate etanx?


Let y= etanx

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

log y = tanx (here we used the logarithm rule logeek =k.)

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

$\dfrac{1}{y} \dfrac{dy}{dx}$ = sec2x as we know that the derivative of tanx is sec2x.

⇒ $\dfrac{dy}{dx}$ = y sec2x

Putting the value of y, that is, y=etanx, we get from above that

$\dfrac{d}{dx}$(etanx) = sec2x etanx.

Thus, the differentiation of etanx with respect to x is equal to etanx sec2x.

Video solution on derivative of etanx:


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.


Q1: What is the derivative of etanx?

Answer: The derivative of e^tanx is equal to sec2x etanx.

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

Answer: If y=etanx, then dy/dx = sec2x etanx.

Spread the love

Leave a Comment