Given that y = (1 +2x) ^ x , prove that dy/dx = y (ln (2x +1) +1 - (1/ (1+2x)) )
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Hello !$\displaystyle y=(1+2x)^x=\exp\left[ x\ln(1+2x) \right]$. Let $\displaystyle u(x)=x\ln(1+2x)$. $\displaystyle y$ can now be written $\displaystyle y=\exp(u(x))$ and the chain rule states that $\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}=u'(x)\exp(u(x))$ : once you have computed $\displaystyle u'$, you are done. Does it help ?