Differentiate f(x) = x/( x + c/x)

Question

Differentiate f(x) = x/( x + c/x)

Answer 1

Mia,

 

let x = h(x) and x + c/x = g(x)

 

Now further break up g(x) in to x² + c and x and lest call them p(x) and q(x).

 

Notice how q(x) = h(x) and that one can be substitute for the other

 

Use "quotient rule" for the first step and leave them in terms of h(x), g(x), h^′(x) and g^′(x) - may not be a good idea to substitute at this point.

 

f^′(x) = [g(x)h^′(x) - g^′(x)h(x)]/[g(x)]²  ------------------------- (1)

 

Get g^′(x) from the second step g^′(x) = [q^′(x)p(x) - p(x)^′q(x)]/[q(x)]²  -------------- (2)

 

Now substitute the g^′(x) from equation 2 in to equation 1 and try to simplify before you plug in the actual terms

 

I hope this helps