Question

Find dy/dx if f(x) = (x + 2)^7x.

Answer 1

$\dfrac{\mathrm d}{\mathrm dx}(x+2)^{7x}=\dfrac{\mathrm d}{\mathrm dx}e^{7x\ln(x+2)}$

By the chain rule, the derivative reduces to

$e^{7x\ln(x+2)}\dfrac{\mathrm d}{\mathrm dx}(7x\ln(x+2))=(x+2)^{7x}\dfrac{\mathrm d}{\mathrm dx}(7x\ln(x+2))$

Then using the product rule, we get

$(x+2)^{7x}\left(7\ln(x+2)+\dfrac{7x}{x+2}\right)$