Calculus Examples

Find dy/dx 6 square root of y^3+1-2x^1.5-2=0
Step 1
Use to rewrite as .
Step 2
Differentiate both sides of the equation.
Step 3
Differentiate the left side of the equation.
Tap for more steps...
Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Evaluate .
Tap for more steps...
Step 3.2.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.2
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 3.2.2.1
To apply the Chain Rule, set as .
Step 3.2.2.2
Differentiate using the Power Rule which states that is where .
Step 3.2.2.3
Replace all occurrences of with .
Step 3.2.3
By the Sum Rule, the derivative of with respect to is .
Step 3.2.4
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 3.2.4.1
To apply the Chain Rule, set as .
Step 3.2.4.2
Differentiate using the Power Rule which states that is where .
Step 3.2.4.3
Replace all occurrences of with .
Step 3.2.5
Rewrite as .
Step 3.2.6
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.7
To write as a fraction with a common denominator, multiply by .
Step 3.2.8
Combine and .
Step 3.2.9
Combine the numerators over the common denominator.
Step 3.2.10
Simplify the numerator.
Tap for more steps...
Step 3.2.10.1
Multiply by .
Step 3.2.10.2
Subtract from .
Step 3.2.11
Move the negative in front of the fraction.
Step 3.2.12
Add and .
Step 3.2.13
Combine and .
Step 3.2.14
Combine and .
Step 3.2.15
Combine and .
Step 3.2.16
Combine and .
Step 3.2.17
Move to the denominator using the negative exponent rule .
Step 3.2.18
Move to the left of .
Step 3.2.19
Combine and .
Step 3.2.20
Multiply by .
Step 3.2.21
Factor out of .
Step 3.2.22
Cancel the common factors.
Tap for more steps...
Step 3.2.22.1
Factor out of .
Step 3.2.22.2
Cancel the common factor.
Step 3.2.22.3
Rewrite the expression.
Step 3.3
Evaluate .
Tap for more steps...
Step 3.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.2
Differentiate using the Power Rule which states that is where .
Step 3.3.3
Multiply by .
Step 3.4
Differentiate using the Constant Rule.
Tap for more steps...
Step 3.4.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.4.2
Add and .
Step 4
Since is constant with respect to , the derivative of with respect to is .
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Solve for .
Tap for more steps...
Step 6.1
Add to both sides of the equation.
Step 6.2
Multiply both sides by .
Step 6.3
Simplify the left side.
Tap for more steps...
Step 6.3.1
Cancel the common factor of .
Tap for more steps...
Step 6.3.1.1
Cancel the common factor.
Step 6.3.1.2
Rewrite the expression.
Step 6.4
Divide each term in by and simplify.
Tap for more steps...
Step 6.4.1
Divide each term in by .
Step 6.4.2
Simplify the left side.
Tap for more steps...
Step 6.4.2.1
Cancel the common factor of .
Tap for more steps...
Step 6.4.2.1.1
Cancel the common factor.
Step 6.4.2.1.2
Rewrite the expression.
Step 6.4.2.2
Cancel the common factor of .
Tap for more steps...
Step 6.4.2.2.1
Cancel the common factor.
Step 6.4.2.2.2
Divide by .
Step 6.4.3
Simplify the right side.
Tap for more steps...
Step 6.4.3.1
Factor out of .
Step 6.4.3.2
Cancel the common factors.
Tap for more steps...
Step 6.4.3.2.1
Factor out of .
Step 6.4.3.2.2
Cancel the common factor.
Step 6.4.3.2.3
Rewrite the expression.
Step 7
Replace with .