Find Dy/dx E^(x/y)=x-y | Mathway

Enter a problem... Calculus Examples Popular Problems Calculus Find dy/dx e^(x/y)=x-y Step 1Differentiate both sides of the equation.Step 2Differentiate the left side of the equation.Tap for more steps...Step 2.1Differentiate using the chain rule, which states that is where and .Tap for more steps...Step 2.1.1To apply the Chain Rule, set as .Step 2.1.2Differentiate using the Exponential Rule which states that is where =.Step 2.1.3Replace all occurrences of with .Step 2.2Differentiate using the Quotient Rule which states that is where and .Step 2.3Differentiate using the Power Rule.Tap for more steps...Step 2.3.1Differentiate using the Power Rule which states that is where .Step 2.3.2Multiply by .Step 2.4Rewrite as .Step 2.5Combine and .Step 3Differentiate the right side of the equation.Tap for more steps...Step 3.1Differentiate.Tap for more steps...Step 3.1.1By the Sum Rule, the derivative of with respect to is .Step 3.1.2Differentiate using the Power Rule which states that is where .Step 3.2Evaluate .Tap for more steps...Step 3.2.1Since is constant with respect to , the derivative of with respect to is .Step 3.2.2Rewrite as .Step 4Reform the equation by setting the left side equal to the right side.Step 5Solve for .Tap for more steps...Step 5.1Multiply both sides by .Step 5.2Simplify.Tap for more steps...Step 5.2.1Simplify the left side.Tap for more steps...Step 5.2.1.1Simplify .Tap for more steps...Step 5.2.1.1.1Cancel the common factor of .Tap for more steps...Step 5.2.1.1.1.1Cancel the common factor.Step 5.2.1.1.1.2Rewrite the expression.Step 5.2.1.1.2Apply the distributive property.Step 5.2.1.1.3Simplify the expression.Tap for more steps...Step 5.2.1.1.3.1Rewrite using the commutative property of multiplication.Step 5.2.1.1.3.2Reorder factors in .Step 5.2.1.1.3.3Move .Step 5.2.1.1.3.4Reorder and .Step 5.2.2Simplify the right side.Tap for more steps...Step 5.2.2.1Simplify .Tap for more steps...Step 5.2.2.1.1Apply the distributive property.Step 5.2.2.1.2Simplify the expression.Tap for more steps...Step 5.2.2.1.2.1Multiply by .Step 5.2.2.1.2.2Reorder and .Step 5.3Solve for .Tap for more steps...Step 5.3.1Add to both sides of the equation.Step 5.3.2Subtract from both sides of the equation.Step 5.3.3Factor out of .Tap for more steps...Step 5.3.3.1Factor out of .Step 5.3.3.2Factor out of .Step 5.3.3.3Factor out of .Step 5.3.4Rewrite as .Step 5.3.5Divide each term in by and simplify.Tap for more steps...Step 5.3.5.1Divide each term in by .Step 5.3.5.2Simplify the left side.Tap for more steps...Step 5.3.5.2.1Cancel the common factor of .Tap for more steps...Step 5.3.5.2.1.1Cancel the common factor.Step 5.3.5.2.1.2Divide by .Step 5.3.5.3Simplify the right side.Tap for more steps...Step 5.3.5.3.1Combine the numerators over the common denominator.Step 5.3.5.3.2Simplify the numerator.Tap for more steps...Step 5.3.5.3.2.1Factor out of .Tap for more steps...Step 5.3.5.3.2.1.1Factor out of .Step 5.3.5.3.2.1.2Factor out of .Step 5.3.5.3.2.1.3Factor out of .Step 5.3.5.3.2.2Rewrite as .Step 5.3.5.3.3Simplify with factoring out.Tap for more steps...Step 5.3.5.3.3.1Factor out of .Step 5.3.5.3.3.2Factor out of .Step 5.3.5.3.3.3Factor out of .Step 5.3.5.3.3.4Rewrite negatives.Tap for more steps...Step 5.3.5.3.3.4.1Rewrite as .Step 5.3.5.3.3.4.2Move the negative in front of the fraction.Step 6Replace with .

Please ensure that your password is at least 8 characters and contains each of the following:

• a number
• a letter
• a special character: @$#!%*?&