Home › JEE Main › mathematics › Continuity and Differentiability › The derivative of $x e^x$ with respect to $x$ is:
The derivative of $x e^x$ with respect to $x$ is:
A$x e^{x-1}$
B$e^x(1 + x)$
C$e^x(x - 1)$
D$e^x$
Answer & Solution
Correct answer: B. $e^x(1 + x)$
Product rule: d/dx(x·eˣ) = 1·eˣ + x·eˣ = eˣ(1+x).
Related questions
Rolle's theorem applies to a function $f$ on $[a, b]$ if $f$ is:The derivative of $ in(3x)$ is:A function differentiable at $x = a$ is always:A function $f$ is continuous at $x = a$ if:The derivative of $ qrt{x}$ with respect to $x$ is:The derivative of $\tan x$ with respect to $x$ is:Rolle's theorem requires that $f$ be continuous on $[a,b]$, differentiable on $(a,b)$ and:A function $f$ is continuous at $c$ only if the left-hand limit, right-hand limit and $f(c