Finding the derivative of a function with a radical

[waffletree]

Homework Statement

Find the differential

Homework Equations

Chain rule : dy/du=dy/du*du/dx
Product rule: f(x)g'(x) + g(x)f'(x)

The Attempt at a Solution

I have tried to move the radical to the top of the equation by making it into an exponent (x^2+1)^-1/2. I then used the product rule and the chain ruleIand i got lost somewhere simplifying it beyond that.

 

[BvU]

Hello Waffle,

PF culture pushes me to ask this

Where were you when you got stuck ? In other words: show us how far you got and why you think you were lost at that point ...

 

[Ray Vickson]

Homework Statement

Find the differential

Homework Equations

Chain rule : dy/du=dy/du*du/dx
Product rule: f(x)g'(x) + g(x)f'(x)

The Attempt at a Solution

I have tried to move the radical to the top of the equation by making it into an exponent (x^2+1)^-1/2. I then used the product rule and the chain ruleIand i got lost somewhere simplifying it beyond that.

Show us what you got. Maybe your final,answer is correct, and maybe it isn't; we cannot tell if you will not show it to us.

 

[Mark44]

Homework Statement

Find the differential

Homework Equations

Chain rule : dy/du=dy/du*du/dx
Product rule: f(x)g'(x) + g(x)f'(x)

The Attempt at a Solution

I have tried to move the radical to the top of the equation by making it into an exponent (x^2+1)^-1/2. I then used the product rule and the chain ruleIand i got lost somewhere simplifying it beyond that.

Please show us what you did. Your steps of using the product rule followed by the chain rule are the right approach.
Also, do you need to find the differential or the derivative? They are related, but not the same.

 

[waffletree]

Please show us what you did. Your steps of using the product rule followed by the chain rule are the right approach.
Also, do you need to find the differential or the derivative? They are related, but not the same.

Sorry I meant to put derivative,
This is where I got stuck at
6x(x^2+1)^-1/2
6x*d/dx(x^2+1)^-1/2+(x^2+1)^-1/2*6
6x*1/2(x^2+1)^-3/2+(x^2+1)^-1/2*6

 

[waffletree]

Hello Waffle,

PF culture pushes me to ask this

Where were you when you got stuck ? In other words: show us how far you got and why you think you were lost at that point ...

Sorry I meant to put derivative,
This is where I got stuck at
6x(x^2+1)^-1/2
6x*d/dx(x^2+1)^-1/2+(x^2+1)^-1/2*6
6x*1/2(x^2+1)^-3/2+(x^2+1)^-1/2*6

 

[Ray Vickson]

Sorry I meant to put derivative,
This is where I got stuck at
6x(x^2+1)^-1/2
6x*d/dx(x^2+1)^-1/2+(x^2+1)^-1/2*6
6x*1/2(x^2+1)^-3/2+(x^2+1)^-1/2*6

$\frac{d}{dx} [(x^2+1)^{-1/2}] = (-1/2) (x^2+1)^{-3/2} \cdot \frac{d}{dx} (x^2+1) = -x(x^2+1)^{-3/2}$.

 

[waffletree]

$\frac{d}{dx} [(x^2+1)^{-1/2}] = (-1/2) (x^2+1)^{-3/2} \cdot \frac{d}{dx} (x^2+1) = -x(x^2+1)^{-3/2}$.

Thank you