Question

Find the derivative of the inverse function
$y = {e}^{x} - 3$
​

Answer 1

Step-by-step explanation:

Given

⇒ y  =  e ×

Taking the natural logarithm of both sides

⇒ ln ( y )  =  ln ( e ×)

By definition of  ln

ln ( a ) = the value.  b , needed to make  e ^b  =  a

(you should memorize this)

therefore

ln ( e × ) =  the value, b , needed to make  e^ b = e ×

that is

In(e×) = x

Therefore  ln ( y )  =  ln ( e × )

implies

x  =  ln ( y )

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