Question

find g'(x) given g(x) = e^x/1-5x

Answer 1

\[g(x) = \frac{ e^x }{ 1-5x }\]

Answer 2

quotient rule?

Answer 3

yes

Answer 4

you should get e^x/(1-5x)^2. If you need additional help I can help you contact me at mathutor101@gmail.com.

Answer 5

so \[e^x * 1-5x - -5 * e^x\]

Answer 6

is that right so far

Answer 7

add parentheses

Answer 8

\[(e^x*1-5x)-(-5*e^x)\]

Answer 9

no

Answer 10

\[e^x(1-5x)-(-5e^x)\]

Answer 11

Okay can I simplify ?

Answer 12

sure...factor out \(e^x\)

Answer 13

(1-5x)-(-5) = \[(1-5x)+5\]

Answer 14

\[e^x(1-5x)-(-5e^x)=e^x(1-5x+5)=e^x(6-5x)\]

Answer 15

that is just the numerator

Answer 16

okay, now how do I find the denominator, I am so lost.

Answer 17

\[\left(\frac{N(x)}{D(x)}\right)'=\frac{D(x)N'(x)-N(x)D'(x)}{D(x)^2}\]

Answer 18

divide by the denominator squared

Answer 19

\[\frac{ e^x(6-5x) }{ (1-5x)^2 }\]

Answer 20

yes

Answer 21

Is that all there is to it? Or is there more?

Answer 22

that is it

Answer 23

Thank You!

Answer 24

No problem