# can someone explain this step (from implicit differentiation question)

• Oct 24th 2012, 09:10 AM
kingsolomonsgrave
can someone explain this step (from implicit differentiation question)
Attachment 25387

I'm not sure how the numerator became 12x^3/2 -1
• Oct 24th 2012, 09:40 AM
Soroban
Re: can someone explain this step (from implicit differentiation question)
Hello, kingsolomonsgrave!

Quote:

$\frac{dy}{dx} \;=\;\frac{6x-\frac{1}{2}x^{-\frac{1}{2}}}{\sin(y)} \quad\Rightarrow\quad \frac{dy}{dx} \;=\; \frac{12x^{\frac{3}{2}}-1}{2\sqrt{x}\sin(y)}\quad\text{How?}$

We have: . $\frac{6x-\frac{1}{2}x^{-\frac{1}{2}}}{\sin(y)}$

Multiply by $\frac{2x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}\!:\;\; \frac{2x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}\cdot \frac{6x-\frac{1}{2}x^{-\frac{1}{2}}}{\sin(y)} \;=\;\frac{12x^{\frac{3}{2}} - 1}{2x^{\frac{1}{2}}\sin(y)}$
• Oct 24th 2012, 09:47 AM
kingsolomonsgrave
Re: can someone explain this step (from implicit differentiation question)
thanks! we know to choose 2x^1/2/2x^1/2 because that will make the 1/2x^-1/2 equal to 1?