Question

Solve,
If f'(x) = Cos(x^2) and y = f [ (2x-1) / (x+1) ], find dy/dx

Answer 1

we may use chain rule

\[y=f(\color{blue}{g(x)}) ~\implies ~\dfrac{dy}{dx}=f'(\color{blue}{g(x)})\times \color{blue}{g'(x)}\]

Answer 2

Okay, I ended up having
dy/dx = f' [ (2x-1) / (x+1) ] x [ 3 / (x+1)^2 ]

Answer 3

looks good, plugin the value of f' [ (2x-1) / (x+1) ]

Answer 4

f'(x) = cos(x^2)

f' [ (2x-1) / (x+1) ] = ?

Answer 5

Would it equal Cos(x^2)? Or do you have to substitute Cos(x^2) into f'?

Answer 6

Like as in
f' [ (2x-1) / (x+1) ] = Cos(x^2)

OR

Cos(x^2) [ (2x-1) / (x+1) ]

Answer 7

not quite, simply replace x by (2x-1) / (x+1)

Answer 8

Ah okay
So like:

Cos( [ (2x-1) / (x+1) ] ^2 ) ?

Answer 9

\[f'(\color{red}{x}) = \cos(\color{red}{x}^2)\]

so

\[f'(\color{red}{ (2x-1) / (x+1) }) = \cos(\color{red}{ [ (2x-1) / (x+1) ] }^2)\]

Answer 10

Ah okay thank you ^^