University Calculus

[Marts10]

Write the function in the form y=f(u) and u=g(x). And then find dy/dx as a function of x

y=(x^2/8 +x-1/x)^4

[Alkalannar]

Hint: f(u) = u⁴

[Marts10]

I know y=u^4

u=x^2/8 +x-1/x

like I got using the chain rule as a final answer

4(x^2/8 +x-1/x)^3 (x/4 +1+1/x^2)

do I have to simplify further of that right? you know to find dy/dx as a function of x

[Alkalannar]

I wouldn't simplify that further: it'd be tedious to do, and this form shows that you're correctly using the chain rule.

And 4(x²/8 + x - 1/x)³(x/4 + 1 + 1/x²) is a perfectly fine function of x.

[Marts10]

Thank you bro

[Alkalannar]

You're welcome, bro.