# How do you differentiate  y = 17(22+x)^((41-x)^30)?

Jun 2, 2018

$y ' = 17 {\left(22 + x\right)}^{{\left(41 - x\right)}^{30}}$

#### Explanation:

Taking the logatithm on both sides we get
$\ln \left(y\right) = \ln \left(17\right) + {\left(41 - x\right)}^{30} \ln \left(22 + x\right)$
differentiating with respect to $x$:

$\frac{y '}{y} = - 30 {\left(41 - x\right)}^{29} \cdot \ln \left(22 + x\right) + {\left(41 - x\right)}^{30} \cdot \frac{1}{22 + x}$
so we get
$y ' = 17 {\left(22 + x\right)}^{{\left(41 - x\right)}^{30}} \left(- 30 \cdot {\left(41 - x\right)}^{29} \cdot \ln \left(22 + x\right) + {\left(41 - x\right)}^{30} / \left(22 + x\right)\right)$