Quotient Rule Calculator

This Quotient Rule Calculator helps you differentiate the quotient of two functions and shows each step clearly. It applies the quotient rule to expressions of the form u(x)/v(x) by differentiating the numerator and denominator and combining them correctly over the square of the denominator. This makes it useful for checking answers, understanding how the rule works, and practising calculus step by step.

Step-by-step method

1. Set up the problem.
2. Differentiate u(x) and v(x).
3. Apply the quotient rule.

Formula:

Example 1: u(x) = x^2+1, v(x) = sin(x)

Step 1 - Set up the problem.

In this problem: We will use u(x) = x^2 + 1 and v(x) = sin(x).

Step 2 - Differentiate u(x) and v(x).

In this problem: Compute u'(x) and v'(x).

Step 3 - Apply the quotient rule.

In this problem: Use (u/v)' = (u'·v − u·v') / v².

Final answer: f'(x) = (2xsin(x) - (x^2 + 1)cos(x))/sin(x)^2

Example 2: u(x) = (1/2)x^3, v(x) = x+1

Step 1 - Set up the problem.

In this problem: We will use u(x) = x^3/2 and v(x) = x + 1.

Step 2 - Differentiate u(x) and v(x).

In this problem: Compute u'(x) and v'(x).

Step 3 - Apply the quotient rule.

In this problem: Use (u/v)' = (u'·v − u·v') / v².

Final answer: f'(x) = (-x^3/2 + 3x^2(x + 1)/2)/(x + 1)^2