courtneymckoon courtneymckoon

21-08-2016
Mathematics

contestada

how to find the derivative of e^3㏑(x²)

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dalendrk dalendrk

28-08-2016

[tex]f(x)=e^{3\ln x^2}\\\\f'(x)=e^{3\ln x^2}\cdot\dfrac{3}{x^2}\cdot2x=e^{3\ln x^2}\cdot\dfrac{6}{x}=\dfrac{6e^{3\ln x^2}}{x}\\\\\\but\ e^{3\ln x^2}=e^{\ln (x^2)^3}=e^{\ln x^6}=x^6\ where\ x\neq0\\\\therefore\ f'(x)=6x^5[/tex]

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