Question

How do you differentiate `(1 / (4-3t)) + ( (3t )/ ((4-3t)^2))`?

Answer 1

Rewrite the expression first.

Explanation:

`1 / (4-3t) + (3t )/ ((4-3t)^2) = (4-3t) / (4-3t)^2 + (3t )/ ((4-3t)^2) = 4/(4-3t)^2`

We can use the quotient rule at this point.

The derivative is:
`((0)(4-3t)^2-(4)[2(4-3t)*(-3)])/((4-3t)^2)^2 =(0+24(4-3t))/(4-3t)^4`

`= 24/(4-3t)^3`

Alternative

If (when) you've learned the chain rule, you may agree that it is easier to continue rewriting to get:

`4/(4-3t)^2 = 4(4-3t)^(-2)`

The derivative is may be found by using the power rule and the chain rule. `-8(4-3t)^(-3)*(-3) = 24(4-3t)^(-3)`