# How do you find the derivative of y= 10^(1-x^2) ?

Jul 26, 2014

The answer is : $y ' = - 2 \ln 10 \cdot x \cdot {10}^{1 - {x}^{2}}$

Solution:

let's $y = {a}^{f} \left(x\right)$, where a is some constant and $f \left(x\right)$ is function of $x$

then, $y ' = {a}^{f} \left(x\right) \ln a \cdot f ' \left(x\right)$

Similarly, if we follow this chain rule, we will get

$y ' = {10}^{1 - {x}^{2}} \ln 10 \cdot \left(- 2 x\right)$

After rearranging, we get

$y ' = - 2 \ln 10 \cdot x \cdot {10}^{1 - {x}^{2}}$