Find the derivative of the following function:

Question

1] f(x) = 2x - 1 / 3x + 2

* / means over*

 

2] f(x) = 1/square root of x

3] f(x) = square root of x^2 - 1

4] f(x) = x^2 + 6x - 3

 

Please show the complete solution. I badly need your help guys. Thankyou!!

Answer 1

1) f(x)=(2x-1)/(3x+2). If u=2x-1 and v=3x+2, du/dx=2 and dv/dx=3.

The derivative is (vdu/dx-udv/dx)/v^2=(2(3x+2)-3(2x-1))/(3x+2)^2=

(6x+4-6x+3)/(3x+2)^2=7/(3x+2)^2

2) f(x)=1/√x=x^(-1/2); f'(x)=-(1/2)x^(-3/2)=-1/√x^3

3) f(x)=√(x^2-1) needs the chain rule:

(1/2)(x^2-1)^(-1/2) * 2x=x/√(x^2-1)

4) f'(x)=2x+6