# Find dy/dx e^(x/y)=5x-y

Differentiate both sides of the equation.
Differentiate the left side of the equation.
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Differentiate using the Quotient Rule which states that is where and .
Differentiate using the Power Rule.
Differentiate using the Power Rule which states that is where .
Multiply by .
Rewrite as .
Differentiate the right side of the equation.
By the Sum Rule, the derivative of with respect to is .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Evaluate .
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 .
Combine and .
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Rewrite using the commutative property of multiplication.
Reorder factors in .
Multiply both sides of the equation by .
Remove parentheses.
Multiply by .
Subtract from both sides of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Combine into one fraction.
Move the negative in front of the fraction.
Combine the numerators over the common denominator.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Simplify with factoring out.
Factor out of .
Factor out of .
Factor out of .
Rewrite negatives.
Rewrite as .
Move the negative in front of the fraction.
Replace with .
Find dy/dx e^(x/y)=5x-y