Joanna3801
Joanna3801
04-05-2017
Mathematics
contestada
Find the derivative of (1+2x)^x^2
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LammettHash
LammettHash
04-05-2017
[tex](1+2x)^{x^2}=e^{\ln(1+2x)^{x^2}}=e^{x^2\ln(1+2x)}[/tex]
Differentiate with the chain rule:
[tex]\dfrac{\mathrm d}{\mathrm dx}e^{x^2\ln(1+2x)}=e^{x^2\ln(1+2x)}\dfrac{\mathrm d}{\mathrm dx}[x^2\ln(1+2x)][/tex]
Use the product rule for the rest:
[tex]e^{x^2\ln(1+2x)}\left(2x\ln(1+2x)+\dfrac{2x^2}{1+2x}\right)=2x\left(\ln(1+2x)+\dfrac x{1+2x}\right)(1+2x)^{x^2}[/tex]
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