If y = e^x x, then dy dx is - Vidyadip

MCQ

If $y = {e^x}\log x$, then ${{dy} \over {dx}}$ is

A
${{{e^x}} \over x}$
B
${e^x}\left( {{1 \over x} + x\log x} \right)$
✓
${e^x}\left( {{1 \over x} + \log x} \right)$
D
${{{e^x}} \over {\log x}}$

✓

Answer

Correct option: C.

${e^x}\left( {{1 \over x} + \log x} \right)$

c
(c) Differentiating $y = {e^x}\log x,$ w.r.t. $x$ ,we get

$\frac{{dy}}{{dx}} = {e^x} \times \frac{1}{x} + \log x \times {e^x} = {e^x}\left( {\frac{1}{x} + \log x} \right)$.

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