d/dx(e^3/3x^2)
2007-10-26 16:02:54 · 3 answers · asked by lovebird 3 in Science & Mathematics ➔ Mathematics
e^3 is a constant, so for now ignore it. Then you have 1/(3x^2), which I will rewrite as (3x^2)^(-1). Take the derivitive of this, which is -6x(3x^2)^(-2). Now multiply by the constant from the beginning: (-6xe^3)/[(3x^2)^(2)]
2007-10-26 16:10:50 · answer #1 · answered by spindoctoradam 3 · 0⤊ 0⤋
Is the function
A. (e^3)/(3x^2)?
If so -- restate it as (e^3)*(1/3)*x^(-2 ) and use the power rule. Note e^3 is just a constant.
The derivative is:
(e^3)*(1/3)*(-2x^(-3)) = -2*(e^3)x^(-3)/3
B. e^(3/3x^2)?
In this case, the 3 cancels out & this is just
e^(3/3x^2) = e^(1/x^2)=e^(x^(-2))
Use the chain rule to dind the derivative
e^(x^(-2))*(-2x^(-3))
2007-10-26 23:16:07 · answer #2 · answered by Ranto 7 · 0⤊ 0⤋
e^3 / 3x^2
quotient rule:
d/dx (u/v) = (u'v - v'u) / v^2
[d/dx (e^3) (3x^2) - d/dx (3x^2) e^3 ] / (3x^2)^2
e^3 is a constant and derivative of a constant is 0
(-6x e^3 ) (e^3) / (9x^4)
simplify
-2e^3 / (3x^3) <== answer
2007-10-26 23:11:21 · answer #3 · answered by Anonymous · 0⤊ 0⤋