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!!!!

Re: Implicit Differentiation Help finding the derivative of this function.

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**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?

Re: Implicit Differentiation Help finding the derivative of this function.

times. we were asked to find the derivative

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

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

Re: Implicit Differentiation Help finding the derivative of this function.

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**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.

Re: Implicit Differentiation Help finding the derivative of this function.

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**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.

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?

Re: Implicit Differentiation Help finding the derivative of this function.

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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?

Re: Implicit Differentiation Help finding the derivative of this function.

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

You would be expected to fully simplify it.