Find dy/dx (xy)^(1/2)=x-2y

Math
Differentiate both sides of the equation.
Differentiate the left side of the equation.
Tap for more steps…
Differentiate using the chain rule, which states that is where and .
Tap for more steps…
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
Multiply by .
Subtract from .
Combine fractions.
Tap for more steps…
Move the negative in front of the fraction.
Combine and .
Move to the denominator using the negative exponent rule .
Differentiate using the Product Rule which states that is where and .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Multiply by .
Simplify.
Tap for more steps…
Apply the product rule to .
Apply the distributive property.
Combine terms.
Tap for more steps…
Combine and .
Move to the numerator using the negative exponent rule .
Multiply by by adding the exponents.
Tap for more steps…
Multiply by .
Tap for more steps…
Raise to the power of .
Use the power rule to combine exponents.
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
Subtract from .
Combine and .
Move to the numerator using the negative exponent rule .
Multiply by by adding the exponents.
Tap for more steps…
Multiply by .
Tap for more steps…
Raise to the power of .
Use the power rule to combine exponents.
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
Subtract from .
Reorder terms.
Differentiate the right side of the equation.
Tap for more steps…
Differentiate.
Tap for more steps…
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Evaluate .
Tap for more steps…
Since is constant with respect to , the derivative of with respect to is .
Rewrite as .
Reform the equation by setting the left side equal to the right side.
Solve for .
Tap for more steps…
Combine and .
Add to both sides of the equation.
Find the LCD of the terms in the equation.
Tap for more steps…
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Since has no factors besides and .
is a prime number
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
The LCM for is the numeric part multiplied by the variable part.
Multiply each term by and simplify.
Tap for more steps…
Multiply each term in by in order to remove all the denominators from the equation.
Simplify each term.
Tap for more steps…
Rewrite using the commutative property of multiplication.
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Tap for more steps…
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by by adding the exponents.
Tap for more steps…
Move .
Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Add and .
Divide by .
Simplify .
Rewrite using the commutative property of multiplication.
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Tap for more steps…
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by by adding the exponents.
Tap for more steps…
Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Add and .
Divide by .
Simplify .
Multiply by .
Multiply by .
Solve the equation.
Tap for more steps…
Subtract from both sides of the equation.
Factor out of .
Tap for more steps…
Move .
Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
Tap for more steps…
Divide each term in by .
Simplify .
Tap for more steps…
Cancel the common factor.
Rewrite the expression.
Cancel the common factor.
Divide by .
Simplify .
Tap for more steps…
Simplify each term.
Tap for more steps…
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Factor out of .
Tap for more steps…
Move .
Factor out of .
Factor out of .
Factor out of .
Replace with .
Find dy/dx (xy)^(1/2)=x-2y

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top