d dx e^ x + 3 x = - Vidyadip

MCQ

${d \over {dx}}{e^{x + 3\log x}} = $

✓
${e^x}.{x^2}(x + 3)$
B
${e^x}.x(x + 3)$
C
${e^x} + {3 \over x}$
D
None of these

✓

Answer

Correct option: A.

${e^x}.{x^2}(x + 3)$

a
(a) ${e^{x + 3\log x}} = {e^x}.{e^{3\log x}} = {e^x}.{e^{\log {x^3}}} = {e^x}.{x^3}$

Therefore $y = {e^x}.{x^3} \Rightarrow \frac{{dy}}{{dx}} = {e^x}.3{x^2} + {x^3}.{e^x} = {e^x}{x^2}(3 + x)$

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