Question

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

Answer 1

`(\mathrm d)/(\mathrm dx)(x+2)^(7x)=(\mathrm d)/(\mathrm dx)e^(7x\ln(x+2))`

By the chain rule, the derivative reduces to


`e^(7x\ln(x+2))(\mathrm d)/(\mathrm dx)(7x\ln(x+2))=(x+2)^(7x)(\mathrm d)/(\mathrm dx)(7x\ln(x+2))`

Then using the product rule, we get


`(x+2)^(7x)\left(7\ln(x+2)+(7x)/(x+2)\right)`