SOLUTION: Please Find the Derivatives of the following and simplify: y=5e^3x y=1/e^x y=e^3 y=e^x2e^2x Thanks!

Question 59236: Please Find the Derivatives of the following and simplify:
y=5e^3x

y=1/e^x

y=e^3

y=e^x2e^2x

Thanks!

Found 2 solutions by venugopalramana, funmath:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Please Find the Derivatives of the following and simplify:
y=5e^3x
DY/DX = 5*3E^3X=15E^3X
y=1/e^x=E^(-X)
DY/DX = -1E^(-X)=-1/E^X
y=e^3 =CONSTANT
DY/DX =0
y=e^x2e^2x
DO YOU MEAN
Y=[E^X][2E^2X]..IF SO
DY/DX = (E^X)[2*2E^(2X)+2E^2X]= 6(E^X)(E^2X)
----IF YOU MEANT [E^(X^2)][E^2X]..THEN
DY/DX = [E^(X^2)]2E^(2X)+[E^2X]2XE^(X^2)=2[E^(X^2)][E^2X][1+X)
Thanks!

Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Find the Derivatives of the following and simplify:
d/dx[cf(x)]=cf'(x)
d/dx[e^x]=e^x
d/dx[c]=0
The chain rule: d/dx[f(g(x)]=f'(g(x))g'(x)
:
Use the chain rule:

:
---->> Use the chain rule again:

:

There is no x, this is a constant even though it doesn't look like one. . The derivative of a constant is 0.

:
I'm not sure if I'm interpretting you right on this one, let me know if there's a misunderstanding!!!
-------->> --->> Use chain rule:

:
Happy Calculating!!!
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