Find dy/dx of y=(x²-7)/(x^1/3). It says I shouldn't have to use the quotient rule and that the final answer should just be in the form ax^m+bx^n. Could someone help me figure this out? Thanks.

Question

anonymous · Answer

Sure, just divide each term in the numerator by the denominator.

$$ \frac{(a+b) }{c} = \frac{a}{c} + \frac{b}{c} $$

anonymous · Answer

That makes more sense. How do you find dy/dx for the exponent that is in the denominator though?

anonymous · Answer

Once fractions get involved, I kinda screw up on these things

anonymous · Answer

Fractions and exponents in the denominator, haha

anonymous · Answer

So that would simplify to 
$$ \frac{x^2-7}{x^{1/3}}  = \frac{x^2}{x^{1/3}} - \frac{7}{x^{1/3}} = x^{2/3} - 7x^{-1/3}$$

anonymous · Answer

why would it be x to the 2/3 power?

anonymous · Answer

Oops, I'm sorry, that should be 5/3, not 2/3

anonymous · Answer

Ah ok that makes sense now. Thanks :)

anonymous · Answer

And then I just need to find dy/dx of that, right?

anonymous · Answer

Right.

anonymous · Answer

Thank you!