Calculus Examples

Find dy/dx y^2=x/(x+1)
Step 1
Differentiate both sides of the equation.
Step 2
Differentiate the left side of the equation.
Tap for more steps...
Step 2.1
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 2.1.1
To apply the Chain Rule, set as .
Step 2.1.2
Differentiate using the Power Rule which states that is where .
Step 2.1.3
Replace all occurrences of with .
Step 2.2
Rewrite as .
Step 3
Differentiate the right side of the equation.
Tap for more steps...
Step 3.1
Differentiate using the Quotient Rule which states that is where and .
Step 3.2
Differentiate.
Tap for more steps...
Step 3.2.1
Differentiate using the Power Rule which states that is where .
Step 3.2.2
Multiply by .
Step 3.2.3
By the Sum Rule, the derivative of with respect to is .
Step 3.2.4
Differentiate using the Power Rule which states that is where .
Step 3.2.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.6
Simplify by adding terms.
Tap for more steps...
Step 3.2.6.1
Add and .
Step 3.2.6.2
Multiply by .
Step 3.2.6.3
Subtract from .
Step 3.2.6.4
Add and .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Divide each term in by and simplify.
Tap for more steps...
Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
Tap for more steps...
Step 5.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Rewrite the expression.
Step 5.2.2
Cancel the common factor of .
Tap for more steps...
Step 5.2.2.1
Cancel the common factor.
Step 5.2.2.2
Divide by .
Step 5.3
Simplify the right side.
Tap for more steps...
Step 5.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 5.3.2
Combine.
Step 5.3.3
Simplify the expression.
Tap for more steps...
Step 5.3.3.1
Multiply by .
Step 5.3.3.2
Move to the left of .
Step 5.3.3.3
Reorder factors in .
Step 6
Replace with .