# Implicit Differentiation Help finding the derivative of this function.

• Oct 4th 2012, 09:05 PM
Mathinik
Implicit Differentiation Help finding the derivative of this function.
Find the derivative of sqrt x = 5 x sqrt y

Answer in the back of the book doesnt make sense to me. d/dx = 1/25

HELPPP!!!!
• Oct 4th 2012, 09:20 PM
Prove It
Re: Implicit Differentiation Help finding the derivative of this function.
Quote:

Originally Posted by Mathinik
Find the derivative of sqrt x = 5 x sqrt y

Answer in the back of the book doesnt make sense to me. d/dx = 1/25

HELPPP!!!!

Is it \displaystyle \displaystyle \begin{align*} \sqrt{x} = 5x\,\sqrt{y} \end{align*} or \displaystyle \displaystyle \begin{align*} \sqrt{x} = 5 \times \sqrt{y} \end{align*}?

Also, were you asked to find the derivative at a POINT, or just the derivative?
• Oct 4th 2012, 09:21 PM
Mathinik
Re: Implicit Differentiation Help finding the derivative of this function.
times. we were asked to find the derivative
• Oct 4th 2012, 09:24 PM
Prove It
Re: Implicit Differentiation Help finding the derivative of this function.
So it's \displaystyle \displaystyle \begin{align*} \sqrt{x} = 5\sqrt{y} \end{align*}. Solving for y gives

\displaystyle \displaystyle \begin{align*} \sqrt{y} &= \frac{1}{5}\sqrt{x} \\ y &= \frac{1}{25} x \\ \frac{dy}{dx} &= \frac{1}{25} \end{align*}
• Oct 4th 2012, 09:28 PM
Mathinik
Re: Implicit Differentiation Help finding the derivative of this function.
Quote:

Originally Posted by Prove It
So it's \displaystyle \displaystyle \begin{align*} \sqrt{x} = 5\sqrt{y} \end{align*}. Solving for y gives

\displaystyle \displaystyle \begin{align*} \sqrt{y} &= \frac{1}{5}\sqrt{x} \\ y &= \frac{1}{25} x \\ \frac{dy}{dx} &= \frac{1}{25} \end{align*}

My instructor said to not solve for y and do what we nomrmally do, take the derivative of each term wit respect to x, and treat y like an x and multiply it with dy/dx.
• Oct 4th 2012, 09:29 PM
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Re: Implicit Differentiation Help finding the derivative of this function.
Quote:

Originally Posted by Mathinik
My instructor said to not solve for y and do what we nomrmally do, take the derivative of each term wit respect to x, and treat y like an x and multiply it with dy/dx.

Then your instructor is a Goober for making you do something the long way when there is very clearly a much simpler way to go about it. You should use Implicit Differentiation ONLY when it would be easier than trying to solve for y and taking the derivative explicitly.
• Oct 4th 2012, 09:36 PM
Mathinik
Re: Implicit Differentiation Help finding the derivative of this function.
so (sqrt y) / (5(sqrt x)) would still be correct if i use implicit differentiation?
• Oct 4th 2012, 09:37 PM
Mathinik
Re: Implicit Differentiation Help finding the derivative of this function.
Quote:

Originally Posted by Prove It
Then your instructor is a Goober for making you do something the long way when there is very clearly a much simpler way to go about it. You should use Implicit Differentiation ONLY when it would be easier than trying to solve for y and taking the derivative explicitly.

so (sqrt y) / (5(sqrt x)) would still be correct if i use implicit differentiation?
• Oct 4th 2012, 09:38 PM
Prove It
Re: Implicit Differentiation Help finding the derivative of this function.
Quote:

Originally Posted by Mathinik
so (sqrt y) / (5(sqrt x)) would still be correct if i use implicit differentiation?

You would be expected to fully simplify it.