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

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

I'm not sure how the numerator became 12x^3/2 -1

2. ## Re: can someone explain this step (from implicit differentiation question)

Hello, kingsolomonsgrave!

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

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

Multiply by $\frac{2x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}\!:\;\; \frac{2x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}\cdot \frac{6x-\frac{1}{2}x^{-\frac{1}{2}}}{\sin(y)} \;=\;\frac{12x^{\frac{3}{2}} - 1}{2x^{\frac{1}{2}}\sin(y)}$

3. ## 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?