Question

Find the derivative of e^-x + sinx - cosx

I just did a calculus test with a bunch of questions... Many of those that had antiderivative and e really confused me...
Please help me to find the answer, but I would also like to know the rules

Answer 1

the derivative of \(e^x\) is \(e^x\) and similarly the anti derivative of \(e^x\) is also \(e^x\)

Answer 2

by the chain rule, the derivative of \(e^{f(x)}\) is \(e^{f(x)}f'(x)\)

Answer 3

for example, the derivative of \(e^{\sin(x)}\) is \(e^{\sin(x)}\cos(x)\)

Answer 4

and the derivative of \(e^{-x}\) is \(-e^{-x}\)

Answer 5

Ah... Thank you so much, those are very useful. I was always troubled by e^f(x) and were not so sure before... thanks!