Calculus Examples

Find dy/dx x^5+y^3=1/y
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.
Tap for more steps...
Step 2.1.1
By the Sum Rule, the derivative of with respect to is .
Step 2.1.2
Differentiate using the Power Rule which states that is where .
Step 2.2
Evaluate .
Tap for more steps...
Step 2.2.1
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 2.2.1.1
To apply the Chain Rule, set as .
Step 2.2.1.2
Differentiate using the Power Rule which states that is where .
Step 2.2.1.3
Replace all occurrences of with .
Step 2.2.2
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 using the Constant Rule.
Tap for more steps...
Step 3.2.1
Multiply by .
Step 3.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.3
Simplify the expression.
Tap for more steps...
Step 3.2.3.1
Multiply by .
Step 3.2.3.2
Subtract from .
Step 3.2.3.3
Move the negative in front of the fraction.
Step 3.3
Rewrite as .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Solve for .
Tap for more steps...
Step 5.1
Multiply both sides by .
Step 5.2
Simplify.
Tap for more steps...
Step 5.2.1
Simplify the left side.
Tap for more steps...
Step 5.2.1.1
Simplify .
Tap for more steps...
Step 5.2.1.1.1
Apply the distributive property.
Step 5.2.1.1.2
Multiply by by adding the exponents.
Tap for more steps...
Step 5.2.1.1.2.1
Move .
Step 5.2.1.1.2.2
Use the power rule to combine exponents.
Step 5.2.1.1.2.3
Add and .
Step 5.2.1.1.3
Move .
Step 5.2.2
Simplify the right side.
Tap for more steps...
Step 5.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.2.2.1.1
Move the leading negative in into the numerator.
Step 5.2.2.1.2
Cancel the common factor.
Step 5.2.2.1.3
Rewrite the expression.
Step 5.3
Solve for .
Tap for more steps...
Step 5.3.1
Add to both sides of the equation.
Step 5.3.2
Subtract from both sides of the equation.
Step 5.3.3
Factor out of .
Tap for more steps...
Step 5.3.3.1
Factor out of .
Step 5.3.3.2
Raise to the power of .
Step 5.3.3.3
Factor out of .
Step 5.3.3.4
Factor out of .
Step 5.3.4
Divide each term in by and simplify.
Tap for more steps...
Step 5.3.4.1
Divide each term in by .
Step 5.3.4.2
Simplify the left side.
Tap for more steps...
Step 5.3.4.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.3.4.2.1.1
Cancel the common factor.
Step 5.3.4.2.1.2
Divide by .
Step 5.3.4.3
Simplify the right side.
Tap for more steps...
Step 5.3.4.3.1
Move the negative in front of the fraction.
Step 6
Replace with .