Question

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

Answer 1

`y'=17(22+x)^((41-x)^30)`

Explanation:

Taking the logatithm on both sides we get
`ln(y)=ln(17)+(41-x)^30ln(22+x)`
differentiating with respect to `x`:

`(y')/ y=-30(41-x)^29*ln(22+x)+(41-x)^30*1/(22+x)`
so we get
`y'=17(22+x)^((41-x)^30)(-30*(41-x)^29*ln(22+x)+(41-x)^30/(22+x))`