# Math Help - derivatives

1. ## derivatives

Find y′ if

y = (10x+3)^6x+7

differentiate both sides with respect to x = ?

solve for y' = ?

2. Originally Posted by pourcarlos
Find y′ if

y = (10x+3)^6x+7

differentiate both sides with respect to x = ?

solve for y' = ?
I assume that you mean:

$y = (10x+3)^{6x+7}$

If so re-write the term of the function to:

$y = e^{(6x+7) \cdot \ln(10x+3)}$

To differentiate this exponential function use chain rule and product rule:

$y'= e^{(6x+7) \cdot \ln(10x+3)} \cdot \left(\ln(10x+3) \cdot 6 + (6x+7) \cdot \dfrac1{10x+3} \cdot 10 \right)$

... and now simplify.