# How do I find the derivative of y= arccos (e^7x)?

Jan 30, 2015

The answer is: y'=-e^7/sqrt(1-e^14x^2

The derivative of the function: $y = \arccos f \left(x\right)$ is

$y ' = - \frac{1}{\sqrt{1 - {\left[f \left(x\right)\right]}^{2}}} \cdot f ' \left(x\right)$.

So:

$y ' = - \frac{1}{\sqrt{1 - {\left({e}^{7} x\right)}^{2}}} \cdot {e}^{7} = - {e}^{7} / \sqrt{1 - {e}^{14} {x}^{2}}$.

A common error is considering ${e}^{n}$ as a function, but it is only a number! Remember that the function is ${e}^{x}$!