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
Two things this chain introduces beside continuity are differentiability and:Composites of continuous functions, by Theorem 2, are:A function that fails the limit test at a point is:To differentiate an implicit relation you use the:The function f(x) = |x| at x = 0 is continuous but not:For f(x) = 2x + 3 at x = 1, the limit and f(1) are both:An alternative to repeated product rule for many factors is:The chain rule can be extended to composites of: