Question

Need help figuring out how to solve this derivative:

Answer 1

\[f(x) = \frac{8e ^{6x} }{ 5x-2 }\]

Answer 2

How do I find f'(x)? Do I apply the quotient rule first or the exponent rule?

PS, that's 8e to 6x... the exponent is a bit hard to see.

Answer 3

firstly you apply the quotient rule.

Answer 4

and watch out at the numerator: \[(\alpha \times x)' = \alpha \times x'\]

Answer 5

[(5x-2)(8e^6x)'] - [(8e^6x)(5x-2)']

Answer 6

Ok, for the first bit, where I have (8e^6x)', is that where I plug in the derivative for the whole numerator?

Answer 7

\[(8e^{6x})' = 8 \times (e^{6x})' = 8 \times e^{6x} \times \ln e \times 6\]

Answer 8

Why? I mean, what are the steps for that part?

Answer 9

well the formula for \[(a^{u})' = a^{u} \times \ln a \times u'\]

Answer 10

I think I got it now, thank you! :)

Answer 11

you're welcome.