- #1

pc2-brazil

- 205

- 3

## Homework Statement

Find dy/dt, given:

[tex]y=x^2-5x+1[/tex]

[tex]x=s^3-2s+1[/tex]

[tex]s=\sqrt{t^2+1}[/tex]

**2. The attempt at a solution**

I am trying to use the chain rule for the case where y is a function of x, x is a function of s and s is a function of t, like below:

[tex]\frac{dy}{dt}=\frac{dy}{dx}\frac{dx}{ds}\frac{ds}{dt}[/tex]

So:

[tex]\frac{dy}{dt}=(2x-5)(3s^2-2)(\frac{t}{\sqrt{t^2+1}})[/tex]

But this gives (substituting x and s for their values as functions of t)

[tex]6t^5-4t^3-\frac{3t}{\sqrt{t^2+1}}-\frac{9t^3}{\sqrt{t^2+1}}-2t[/tex]

which is not the correct result. The correct result is:

[tex]6t^5-4t^3-9t\sqrt{t^2+1}+\frac{6t}{\sqrt{t^2+1}}-2t[/tex]

What is wrong?

Thank you in advance.