# Thread: Implicit Differentiation of a Function

1. ## Implicit Differentiation of a Function

Find the indicated derivative through implicit differentiation:

$\displaystyle a^4-t^4 = 6a^2t$; da/dt = ?

$\displaystyle 4a^3da/dt - 4t^3 = 12a*da/dt$

I took the terms with da/dt to one side, took common and then divided to the other side to get:

$\displaystyle \frac{-t^3}{3a-a^3}$

Which is not the real answer:
$\displaystyle \frac{2t^3+3a^2}{2a^3-6at}$

2. Originally Posted by StarlitxSunshine
Find the indicated derivative through implicit differentiation:

$\displaystyle a^4-t^4 = 6a^2t$; da/dt = ?

$\displaystyle 4a^3da/dt - 4t^3 = 12a*da/dt$

This is not implicit, or any other, differentiation! You must do:

$\displaystyle 4a^3da-4t^3dt=12atda+6a^2dt$ , and then gather togeter simmilar terms and stuff.

Tonio

I took the terms with da/dt to one side, took common and then divided to the other side to get:

$\displaystyle \frac{-t^3}{3a-a^3}$

Which is not the real answer:
$\displaystyle \frac{2t^3+3a^2}{2a^3-6at}$
.

3. How can you separate da & dt ?

4. Originally Posted by StarlitxSunshine
How can you separate da & dt ?

Gather simmilar terms together and use parentheses!

Tonio