Question

how to find indicated derivative of \frac{6t^3+3}{t^4}

Answer 1

\[\frac{6t^3+3}{t^4}\]

Answer 2

Familiar with the quotient rule?

Answer 3

when all of my answr. choices are fractions though.

Answer 4

they look like -6/t - 12/t^5

Answer 5

Yes, the differentiation will be a rational function. Have you been over the quotient rule?

Answer 6

i am familiar with the quo rule. but isnt there a simpler way to solve this to match the formatting of my answr choices?

Answer 7

\[(6t^2+3)t^{-4}\] and you can do product rule but the trick here is to remember chain rule

Answer 8

Yea, you can either do what @2le suggested, or you can also split the fraction up into a sum of much prettier and easier to differentiate fractions. But you still have to apply the quotient rule twice.

Answer 9

how do i "split the fraction"

Answer 10

\[\frac{6x^3}{x^4} + \frac{3}{x^4}\]
You can reduce the one on the left to:
\[\frac{6}{x}\]

Answer 11

So you have some really easy fractions to differentiate there, but yes. You still have to apply the quotient rule to both.

Answer 12

oh wow i see. thank you

Answer 13

@2le thank you also !