# Problem in applying the Chain Rule

Gold Member

## 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!

#### Attachments

• Delta2

fresh_42
Mentor
2021 Award

## 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 Helper
Dearly Missed

## 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
Delta2
Homework Helper
Gold Member
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}##.

• navneet9431