Answer to Question #143964 in Calculus for liam donohue

Question

Differentiate the following function: f(x)=ex+xe

Answer 1

$f(x) = e^x + xe^x\\ \textsf{differentiating }e^x\textsf{, we get }e^x$

$\textsf{differentiating } xe^x\textsf{, we use the product rule}\\ \textsf{let u} = x\\ \textsf{let v} = e^x\\ du = 1\\ dv = e^x\\ \textsf{from, }Udv+ Vdu\\ \textsf{we get }xe^x + e^x \textsf{ as the differentiated solution}$

Substituting the differentiated value back into the original question, we have;

$f'(x) = (e^x) + (xe^x + e^x)\\ f'(x) = 2e^x + xe^x\\ \therefore f'(x) = e^x(x+2)$