Find y′ if
y = (10x+3)^6x+7
differentiate both sides with respect to x = ?
solve for y' = ?
I assume that you mean:
$\displaystyle y = (10x+3)^{6x+7}$
If so re-write the term of the function to:
$\displaystyle y = e^{(6x+7) \cdot \ln(10x+3)}$
To differentiate this exponential function use chain rule and product rule:
$\displaystyle y'= e^{(6x+7) \cdot \ln(10x+3)} \cdot \left(\ln(10x+3) \cdot 6 + (6x+7) \cdot \dfrac1{10x+3} \cdot 10 \right)$
... and now simplify.