Differentiate this:?

Question

Differentiate e^sin x sin e^x with respect to x

Answer 1

y = e^(sin x) sin (e^x)
y' = e^(sin x) (sin(e^x))' + (e^(sin x))' sin(e^x)
y' = e^(sin x)cos(e^x)(e^x) + e^(sin x)(cos x)sin(e^x)
y' = e^(sin x)(e^x cos(e^x) + cos x sin(e^x))

Answer 2

Let say x = 90
Then e^ sinx = e^sin90 = e^1 = e ------------------------------------ (1)

Whereas,
Sin e^x = Sin e^90 = ………(Find from log table) which would definitely greater than 1 -------------------(2)

Thus from 1 & 2
e^sin x < sin e^x

Answer 3

the question is not clear... make sure you put on some brackets next time you aska question....

differentiation tips:
sin x -->cos x
e^sinx --> (cosx) . (e^sinx)

Answer 4

I'd love to try, but it isn't clear exactly what your function is.

Answer 5

Is that [e^(sin x)][sin(e^x)] ?

It's D[e^(sin x)][sin(e^x)] + [e^(sin x)](D[sin(e^x)]) =

[e^(sin x)][cosx][sin(e^x)] + [e^(sin x)][cos(e^x)](e^x) =


[e^(sin x)]{[cosx][sin(e^x)] + [cos(e^x)](e^x)}