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ta123
need help with the following attachment
I think the answer is cos(e^(t)) e^(t)+e^(sin t)sin
Looks like chain rule: For sin(e^t), u=e^t and du=e^t Substitute e^t with u and derive sin(u), then multiply by du: cos(u)*du Replace u & du: cos(e^t)*e^t For e^sin(t), u=sin(t) and du=cos(t) Substitute sin(t) with u and derive e^u, then multiply by du: e^u*du Replace u & du: e^sin(t)*cos(t) So you're entire answer is: \[\cos(e^t)*e^t + e^{\sin(t)}*\cos(t)\]