How do you find the derivative of $y = e^{x} \cdot ln x$ $y=e^x*lnx$ ?

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How do you find the derivative of $y = e^{x} \cdot ln x$ $y=e^x*lnx$ ?

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Answer 1 · 2017-05-30T12:31:58

$\frac{d y}{d x} = e^{x} (ln x + \frac{1}{x})$ $dy/dx=e^x(lnx+1/x)$

Explanation:

$differentiate using the product rule$ $"differentiate using the "color(blue)"product rule"$

$Given y = g (x) h (x) then$ $"Given " y=g(x)h(x)" then"$

$dy/dx=g(x)h'(x)+h(x)g'(x)larr" product rule"$

$"here " g(x)=e^xrArrg'(x)=e^x$

$h(x)=lnxrArrh'(x)=1/x$

$rArrdy/dx=e^x. 1/x+lnx.e^x$

$color(white)(rArrdy/dx)=e^x(lnx+1/x)$

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How do you find the derivative of $y = e^{x} \cdot ln x$ $y=e^x*lnx$ ?

1 Answer

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How do you find the derivative of $y = e^{x} \cdot ln x$ $y=e^x*lnx$ ?