Find dy/dx by implicit differentiation.

x^8+9x+x^13y-y^3=9

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Have you not even tried to do this yourself? Are you taking a Calculus course? Do you know what a derivative is?

What is the derivative of x^8 with respect to x?

What is the derivative of 9x with respect to x?

What is the derivative of x^13 with respect to x?

What is the derivative of y with respect to x? (Since you are not told how y is a function of x you can only answer y' or dy/dx.)

So, using the product rule, what is the derivative of x^13y with respect to x?

What is the derivative of y^3 with respect to y? So, using the chain rule, what is the derivative of y^3 with respect to x? (Again, you will have a y' or dy/dx.)

What is the derivative of the constant, 9, with respect to x?

Putting all of those together, what is the derivative of the equation x^8+ 9x+ x^13y+ y^3= 9?

(In other words, the derivatives of the two sides set equal.)

Solve that equation for y' or dy/dx, whichever you chose to use.

What is the derivative of x^8 with respect to x?

What is the derivative of 9x with respect to x?

What is the derivative of x^13 with respect to x?

What is the derivative of y with respect to x? (Since you are not told how y is a function of x you can only answer y' or dy/dx.)

So, using the product rule, what is the derivative of x^13y with respect to x?

What is the derivative of y^3 with respect to y? So, using the chain rule, what is the derivative of y^3 with respect to x? (Again, you will have a y' or dy/dx.)

What is the derivative of the constant, 9, with respect to x?

Putting all of those together, what is the derivative of the equation x^8+ 9x+ x^13y+ y^3= 9?

(In other words, the derivatives of the two sides set equal.)

Solve that equation for y' or dy/dx, whichever you chose to use.

- HallsofIvy
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