How do you find the derivative of y=2(5x+3)^7-1 using the chain rule?

Feb 4, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = 70 {\left(5 x + 3\right)}^{6}$

Explanation:

Note: derivative of a constant is zero so $\frac{d}{\mathrm{dx}} \left(- 1\right) = 0$

differentiate using the $\textcolor{b l u e}{\text{ chain rule}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 7 \cdot 2 {\left(5 x + 3\right)}^{6} \frac{d}{\mathrm{dx}} \left(5 x + 3\right) = 14 \left(5 x + 3\right) \cdot 5$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = 70 {\left(5 x + 3\right)}^{6}$