Finding the Derivative of a Function with Implicit Differentiation

[Quadruple Bypass]

Assume that y is a function of x . Find y' = dy/dx for (x^3+y^3)^20

when i solved this i got y'= (20(x^3+y^3)^19 * 3x^2)/(-3y^2)

is this correct or am i missing something?

 

[TD]

It's not entirely right, remember that y(x) is an unknown function of x!

<br /> \begin{gathered}<br /> y = \left( {x^3 + y^3 } \right)^{20} \hfill \\<br /> y&#039; = 20\left( {x^3 + y^3 } \right)^{19} \cdot \left( {x^3 + y^3 } \right)^\prime = 20\left( {x^3 + y^3 } \right)^{19} \cdot \left( {3x^2 + 3y^2 \cdot y&#039;} \right) \hfill \\ <br /> \end{gathered} <br />

Now you can solve for y'.

 

[Quadruple Bypass]

thanks a lot man. the grader only took off 3 pts for that prob and didnt say anything else, so i didnt know what i did wrong.

THANKS A LOT, you just saved me from making several mistakes on my final exam tommorow :D

 

[TD]

Good luck!