[tex]\dfrac{\mathrm d}{\mathrm dx}(x+2)^{7x}=\dfrac{\mathrm d}{\mathrm dx}e^{7x\ln(x+2)}[/tex]
By the chain rule, the derivative reduces to
[tex]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))[/tex]
Then using the product rule, we get
[tex](x+2)^{7x}\left(7\ln(x+2)+\dfrac{7x}{x+2}\right)[/tex]
