Home > Calculus > Quotient Rule

How do you integrate #f(x)=(2x+1)/(3x-4)# using the quotient rule?

Answer 1

Samantha Adkison

There is no quotient rule for integration.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Adam Adkins

To integrate ( f(x) = \frac{2x+1}{3x-4} ) using the quotient rule, you would first rewrite the function as ( f(x) = (2x+1)(3x-4)^{-1} ). Then, you would apply the quotient rule, which states that the derivative of ( \frac{u(x)}{v(x)} ) is ( \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} ). Applying this rule to the function ( f(x) ), where ( u(x) = 2x+1 ) and ( v(x) = 3x-4 ), you would get:

[ f'(x) = \frac{(2)(3x-4) - (2x+1)(3)}{(3x-4)^2} ]

Simplify the expression:

[ f'(x) = \frac{6x - 8 - 6x - 3}{(3x-4)^2} ]

[ f'(x) = \frac{-11}{(3x-4)^2} ]

So, the derivative of ( f(x) ) is ( \frac{-11}{(3x-4)^2} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.