Find the following derivatives using the definition of the derivative

Question

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

(b) √2x+1

(c) (1)/(x²)

Answer 1

Part a

 

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

 

Part b

 

2x^½ +1

 

Now use the power rule.

 

y'=x^-½

 

Part c

 

x^-2  and use power rule

 

y'=-2x^-3