Question

Find the derivative of

x^(x+17)

y ' = _______

how do I start this?

Answer 1

oh and you simplify it from there to get just (x+17)(x^(x+16)) ?

Answer 2

ahh okay awesome!! thank you!!

Answer 3

:/ that's not how the power rule works. The power is not constant.

Answer 4

let \[y=x ^{x+17},\ln y=\ln x ^{x+17}=\left( x+17 \right)\ln x\]
diff.w.r.t. x
\[\frac{ y' }{ y }=\left( x+17 \right)*\frac{ 1 }{ x }+\ln x*\left( 1 \right)\]
\[y'=y \left\{ \frac{ x+17 }{ x }+\ln x \right\}\]
\[\frac{ dy }{ dx }=x ^{x+17}\left\{ \frac{ x+17 }{ x }+\ln x \right\}\]

Answer 5

ohhh okay i see.. thank you!!

Answer 6

Whenever you have an x in exponent, you'll very likely have to use ln on both sides, to differentiate the function.

Answer 7

ahh okay, awesome!Thanks @agent0smith @surjithayer :)

Answer 8

yw