Calculus Examples

Find dy/dx y = square root of x(x-1)
Step 1
Use to rewrite as .
Step 2
Differentiate both sides of the equation.
Step 3
The derivative of with respect to is .
Step 4
Differentiate the right side of the equation.
Tap for more steps...
Step 4.1
Differentiate using the Product Rule which states that is where and .
Step 4.2
Differentiate.
Tap for more steps...
Step 4.2.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2.2
Differentiate using the Power Rule which states that is where .
Step 4.2.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.2.4
Simplify the expression.
Tap for more steps...
Step 4.2.4.1
Add and .
Step 4.2.4.2
Multiply by .
Step 4.2.5
Differentiate using the Power Rule which states that is where .
Step 4.3
To write as a fraction with a common denominator, multiply by .
Step 4.4
Combine and .
Step 4.5
Combine the numerators over the common denominator.
Step 4.6
Simplify the numerator.
Tap for more steps...
Step 4.6.1
Multiply by .
Step 4.6.2
Subtract from .
Step 4.7
Move the negative in front of the fraction.
Step 4.8
Combine and .
Step 4.9
Move to the denominator using the negative exponent rule .
Step 4.10
Simplify.
Tap for more steps...
Step 4.10.1
Apply the distributive property.
Step 4.10.2
Combine terms.
Tap for more steps...
Step 4.10.2.1
Combine and .
Step 4.10.2.2
Move to the numerator using the negative exponent rule .
Step 4.10.2.3
Multiply by by adding the exponents.
Tap for more steps...
Step 4.10.2.3.1
Multiply by .
Tap for more steps...
Step 4.10.2.3.1.1
Raise to the power of .
Step 4.10.2.3.1.2
Use the power rule to combine exponents.
Step 4.10.2.3.2
Write as a fraction with a common denominator.
Step 4.10.2.3.3
Combine the numerators over the common denominator.
Step 4.10.2.3.4
Subtract from .
Step 4.10.2.4
Rewrite as .
Step 4.10.2.5
To write as a fraction with a common denominator, multiply by .
Step 4.10.2.6
Combine and .
Step 4.10.2.7
Combine the numerators over the common denominator.
Step 4.10.2.8
Move to the left of .
Step 4.10.2.9
Add and .
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Replace with .