Find the derivative of y = sin(xe^x) with respect to x.

Use the chain rule: the derivative of sin(u) is cos(u) × du/dx. Here u = xe^x.

For u, use the product rule: d/dx (x · e^x) = 1 · e^x + x · e^x = e^x + xe^x.

So dy/dx = cos(xe^x)(e^x + xe^x).

The cosec and sec options are wrong because the derivative of sin is cos, with no minus sign.