What is the derivative with respect to x of
e^2x
2006-11-08 08:13:45 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
2*(e^2x)
Chain rule.
2006-11-08 08:16:10 · answer #1 · answered by THJE 3 · 0⤊ 0⤋
e^2x = e^x * e^x = (e^x)²
d/dx e^2x = d/dx e^x * e^x
Now just use the product rule:
d/dx e^x * e^x = (e^x * d/dx e^x) + (e^x * d/dx e^x)
= (e^x * e^x) + (e^x * e^x)
= (e^x)² + (e^x)²
= 2(e^x)²
= 2e^(2x)
I know I could have done it a lot faster with the chain rule, but I didn't want to do it the same way everyone else did it.
2006-11-08 16:23:29 · answer #2 · answered by عبد الله (ドラゴン) 5 · 0⤊ 0⤋
the derivative of e^y is e^y * (the derivative of y)
in this case its e^(2x) * (derivative of 2x) = e^(2x) * 2 = 2e^(2x)
2006-11-08 16:20:40 · answer #3 · answered by fanis t 2 · 0⤊ 0⤋
2 * e ^ 2x
2006-11-08 16:15:10 · answer #4 · answered by mike 1 · 1⤊ 0⤋
2e^2x
2006-11-08 16:16:35 · answer #5 · answered by kula o 2 · 0⤊ 0⤋