Implicit Differentiatoin question

[compute_a_nerd]

Hello all.
I am given the equation $$(x^3 y^4)^5 = x-y$$

my derivative is $$1/ (15x^2 20y^3(x^3y^4)^4)=y'$$

But the book says: $$y'=(1-15x^14y^20)/(1+20x^15y^19)$$

Where did I go wrong?

Thanks so much
Chris

 

[Tide]

You didn't differentiate the left side correctly. Try again.

 

[Fermat]

...

But the book says: $$y'=(1-15x^14y^20)/(1+20x^15y^19)$$

...
Chris

You need to put curly brackets around all of your power if there is more than one character involved - like so,

$$y'=(1-15x^{14}y^{20})/(1+20x^{15}y^{19})$$