Joanna3801 Joanna3801
  • 04-05-2017
  • Mathematics
contestada

Find the derivative of (1+2x)^x^2

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LammettHash
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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