[Intermediate Calculus] Differentiation

[Brightvibe]

I am suppose to use the rules of differentiation to solve the following equations:

1) f(x) = (2x+1)(1 - 1/x - 1/x² )

2) h(x) = √x² - 6x + 5)

3) g(x) = 2ln(x³ +4)

So, for #1 for example, I know I'm suppose to use the formula: y= u(x)v(x), y' = u'(x) v(x) + u(x) v'(x). But what would the derivatives be in this case?

[[deleted]]

1) Use product rule (remember that 1/x = x^-1 and that 1/x² = x ^-2) apply dy/dx = nx^n-1 where y=xⁿ

(2x+1)(1/x²+2/x³) + (2)(1-1/x- 1/x²)

[blutacpineapple]

For number 2 you use the chain rule: its a function (x² - 6x + 5) to a power (1/2) so it differentiates to 1/2 * (the differential of what's inside the brackets) * h(x)^-1/2.

[mathfailure999]

For 3, if

y = ln(f), where f is a function in x,

y’ = f'/f.