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 or ?

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 . Solving for y gives

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

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Originally Posted by

**Prove It** So it's

. Solving for y gives

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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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.

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.

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?

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

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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.