Find Derivative using definition of derivative

Question

a.) (x+1)/(x-1)

b.) √(2x+1)

c.) 1/x^2

Answer 1

Part a

 

Use the quotient rule:  (derivative of f(x)*g(x)-[f(x)*derivative g(x)])/(g²(x))  , where f(x) = x+1 and g(x) = x-1

 

Part b

 

Use the chain rule: derivative of the inside function multiplied by the derivative of outside function evaluated inside.

Rewrite √(2x+1) as (2x+1)^½.

 

You end up with 2*(1/2)(2x+1)^-½.

 

Part c

 

Use the power rule:  Multiply the function by the base and subtract exponent by 1.

Rewrite the function 1/x² as  x^-2.

 

You end up with -2x^-3.