Thread: dy/dx y=e^(3x)*sin(pi*x)

1. dy/dx y=e^(3x)*sin(pi*x)

How can I figure this out? I feel dumb.

Derivitive of
y= e to the power 3x, times the sin of (pi times x)
y=e^(3x)*sin(pi*x)

2. Originally Posted by Terrible Idiot
How can I figure this out? I feel dumb.

Derivitive of
y= e to the power 3x, times the sin of (pi times x)
y=e^(3x)*sin(pi*x)
You do it by the product rule.

To refresh your memory, the product rule says, if you have two functions a,b multiplied by each other, then their derivative is given by:

d/dx(ab) = a'b + b'a

In other words, it is the derivative of the first function times the second plus the derivative of the second function times the first. (of course the order doesn't matter, you can take the derivative of the second function first and so on...). Note, you also need the chain rule for this, since you have e^(3x) instead of e^x and sin(pi*x) instead of sin(x)

y = y=e^(3x)*sin(pi*x)
=> y' = 3e^(3x)*sin(pi*x) + pi*e^(3x)cos(pi*x)
= e^(3x)*(3sin(pix) + pi*cos(pix))

P.S. Don't call yourself a Terrible Idiot, nothing comes easy the first time around

3. Thanks Jhevon.