Problem in applying the Chain Rule

[navneet9431]

Homework Statement

I am facing problem in applying the chain rule.
The question which I am trying to solve is,
" Find the second derivative of

"

Homework Equations

The Attempt at a Solution

So, differentiated it the first time,

[BY CHAIN RULE]

And now to find the second derivative I differentiated it once again,
so,

=>

But this is a wrong answer.
Please tell me where am I doing the mistake in applying the chain rule?
I will be thankful for help!

 

[fresh_42]

Homework Statement

I am facing problem in applying the chain rule.
The question which I am trying to solve is,
" Find the second derivative of View attachment 227541 "

Homework Equations

View attachment 227542

The Attempt at a Solution

So, differentiated it the first time,
View attachment 227543 [BY CHAIN RULE]
View attachment 227544
And now to find the second derivative I differentiated it once again,
so,
View attachment 227545
=>View attachment 227546
But this is a wrong answer.
Please tell me where am I doing the mistake in applying the chain rule?
I will be thankful for help!

You differentiated $\dfrac{d}{dx}(fg)$ to $\dfrac{d}{dx}(f)\cdot \dfrac{d}{dx}(g)$ which it is not, and it is not the chain rule.
Do you know the chain rule? I would have expected this information under point 2. of the template.

 

[Ray Vickson]

Homework Statement

I am facing problem in applying the chain rule.
The question which I am trying to solve is,
" Find the second derivative of View attachment 227541 "

Homework Equations

View attachment 227542

The Attempt at a Solution

So, differentiated it the first time,
View attachment 227543 [BY CHAIN RULE]
View attachment 227544
And now to find the second derivative I differentiated it once again,
so,
View attachment 227545
=>View attachment 227546
But this is a wrong answer.
Please tell me where am I doing the mistake in applying the chain rule?
I will be thankful for help!

To get $d^2y/dt^2$ you need to apply the product rule to $dy/dt$. That will produce two terms, not one, although you can then simplify it down to one term again.

Please do NOT attach images; it makes it difficult to cite results and sub-results. Since you already used some kind of package to format your formulas, why not type them in here directly, using LaTeX?

 

[Delta2]

Your mistake is not in the application of the chain rule but you don't seem to apply correctly the product rule. You have find $\frac{dy}{dt}$ as product of $t$ and $(t^2+1)^{-\frac{1}{2}}$. So to calculate the derivative of that product first apply correctly the product rule $\frac{d(fg)}{dt}=\frac{df}{dt}g+f\frac{dg}{dt}$ for $f(t)=t$ and $g(t)=(t^2+1)^{-\frac{1}{2}}$and then apply the chain rule to calculate correctly $\frac{dg}{dt}$.