Find the first derivative?

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tedog1985

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Feb 27, 2006
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I have this problem i cant figure out to do.


Find the First Derivative of

y = 2x^3 e^3x+5


Can anyone help me? THanks for your time
 
You need some ()s. Can't tell if it is
2x^3 e^3x+5 or
(2x)^3 * e^3x+5 or
2*x^3 * e^(3x)+5 or
2x^3 * e^(3x+5) or
?
In any case you would use the product rule to get the derivitive.
 
I guess you are saying you know PEMDAS and are using it.
2x^3 e^3x+5 =
2x³*e³*x + 5 =
2e³*(x^4)+5 and you don't need the product rule.
d(2e³*(x^4)+5) =
2e³*4x³ * dx =
8e³x³ * dx
 
Ok, we're back to the product rule.
d(uv) = uv'+vu' where
u = 2x³
u'=6x²
v=e^(3x+5)
v' = (3x+5)e^(3x+5)
Take it from there.
 
THis is what the problem looks like. I need help with this? HELP!!!

http://imageshack.us

untitled15gp.jpg
 
Yes, that's the problem I gave you the product rule for. Where are you lost?
 
ok figured this out now Thanks for your help Gene im a self study student and this is kicking my butt thanks again
 
Ok this is what im getting for this problem now. Can someone check my work to see if this is correct

Y(x)= f(x)g(x)

dY/dx = df/dx g(x) + dg/dx f(x) [product rule]

f(x) = 2x3 and g(x) = e3x+5

df/dx = 3*2x3-1 = 6x2 and dg/dx = e3x+5*3 = 3e3x+5

putting values in the product rule formula:

dY/dx = 6x2(e3x+5) + 3e3x+5(2x3)

dY/dx = 6x2(e3x+5) + 6x3(e3x+5)

dY/dx = 6x2(e3x+5)[1 + x]
 
Y(x)= f(x)g(x)
dY/dx = df/dx g(x) + dg/dx f(x) f(x) = 2x^3 and g(x) = e^(3x+5)
Fine this far
df/dx = 3*2x^3-1 = 6x^2 and
The red part is wrong tho the 6x^2 is right
dg/dx = 3*e(3x+5)
Good catch. I had a mental lapse and v' = (3x+5)e^(3x+5) should have been
v' = 3*e^(3x+5) as you say.
dY/dx = df/dx g(x) + dg/dx f(x)
dY/dx = (6x^2)*e(3x+5) + 3e^(3x+5)(2x^3)
dY/dx = 6x^2*e(3x+5) + 6x^3*e(3x+5)

dY/dx = 6x^2*e^(3x+5)[1 + x]
After correcting the typing it looks right

PS. Put this in your favorites. It covers how to type math.
 
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