Find y' of e^x + x^e?

Question

Is it just reducing it one power each?

y' = xe^x-1 + ex^e-1?

Answer 1

The second part is right, but for e^x, the derivative is just e^x... d/dx (e^u) = e^u (du/dx) (don't forget, if the exponent is something besides just x, you need to use the chain rule)
The power reducing only works for a variable raised to a power. e, although it is a letter, is actually a number, or a constant, not a variable.

so, y' = e^x + e*x^(e-1)

Answer 2

y' = e^x + e*x^(e-1)

Answer 3

y= e^x + x^e
dy/dx = e^x + e.x^(e-1)

For the function e^x, the derivative is the same (i.e. e^x) by definition(try the MacLaurin expansion and differentiate term by term, or alternatively the fact that the function has a derivative the same as the function may be taken as a definition at elementary level.
Hope this helps!

Answer 4

Given,

y = e^x + x^e

=> y' = e^x + ex^(e-1)

Answer 5

That's right for the second half, not the first tho.

y' = e^x + ex^(e - 1)

The derivative of e^x is just e^x.

Answer 6

e^x + ex^(e-1)

Answer 7

y = e^x + x^e

y' = e^x + ex^(e-1)

Answer 8

(e^x + x^e)' = e^x + e*x^(e-1)
you made it right