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The derivative of e^(3x + 4) w.r.te e^...

The derivative of `e^(3x + 4) ` w.r.te ` e^(4x)` is

A

`(3)/(4) e^(4-x)`

B

`(4)/(3) e^(4-x)`

C

`(3)/(4) e^(x-4)`

D

`(4)/(3) e^(x-4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` u = e^(3x + 4) and v= e^(4x)`
Then, ` (du)/(dx) e^(3x + 4) . 3 and (dv)/(dx) = e^(4x) . 4 `
Now , ` (du)/(dv) = (3 . e^(3x + 4))/(4.e^(4x)) = (3)/(4) e^(3x + 4 - 4x )`
`(3)/(4) e^(4-x)` .
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