can someone explain this step (from implicit differentiation question)

**kingsolomonsgrave** · October 24th 2012, 08:10 AM

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

**Soroban** · October 24th 2012, 08:40 AM

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

**kingsolomonsgrave** · October 24th 2012, 08:47 AM

thanks! we know to choose 2x^1/2/2x^1/2 because that will make the 1/2x^-1/2 equal to 1?

Thread: can someone explain this step (from implicit differentiation question)

LinkBack

Thread Tools

Display

can someone explain this step (from implicit differentiation question)

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

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

Similar Math Help Forum Discussions

implicit differentiation problem step by step (tell me if my concepts are wrong plz)

kindly explain the step

Please explain this step

integral - can someone explain this question step by step plz and thank you

Please explain step by step

Search Tags