Calculus Examples - Mathway

Enter a problem... Calculus Examples Popular Problems Calculus Find dy/dx e^(xy)+x^2-y^2=10 Step 1Differentiate both sides of the equation.Step 2Differentiate the left side of the equation.Tap for more steps...Step 2.1By the Sum Rule, the derivative of with respect to is .Step 2.2Evaluate .Tap for more steps...Step 2.2.1Differentiate using the chain rule, which states that is where and .Tap for more steps...Step 2.2.1.1To apply the Chain Rule, set as .Step 2.2.1.2Differentiate using the Exponential Rule which states that is where =.Step 2.2.1.3Replace all occurrences of with .Step 2.2.2Differentiate using the Product Rule which states that is where and .Step 2.2.3Rewrite as .Step 2.2.4Differentiate using the Power Rule which states that is where .Step 2.2.5Multiply by .Step 2.3Differentiate using the Power Rule which states that is where .Step 2.4Evaluate .Tap for more steps...Step 2.4.1Since is constant with respect to , the derivative of with respect to is .Step 2.4.2Differentiate using the chain rule, which states that is where and .Tap for more steps...Step 2.4.2.1To apply the Chain Rule, set as .Step 2.4.2.2Differentiate using the Power Rule which states that is where .Step 2.4.2.3Replace all occurrences of with .Step 2.4.3Rewrite as .Step 2.4.4Multiply by .Step 2.5Simplify.Tap for more steps...Step 2.5.1Apply the distributive property.Step 2.5.2Reorder terms.Step 3Since is constant with respect to , the derivative of with respect to is .Step 4Reform the equation by setting the left side equal to the right side.Step 5Solve for .Tap for more steps...Step 5.1Reorder factors in .Step 5.2Move all terms not containing to the right side of the equation.Tap for more steps...Step 5.2.1Subtract from both sides of the equation.Step 5.2.2Subtract from both sides of the equation.Step 5.3Factor out of .Tap for more steps...Step 5.3.1Factor out of .Step 5.3.2Factor out of .Step 5.3.3Factor out of .Step 5.4Divide each term in by and simplify.Tap for more steps...Step 5.4.1Divide each term in by .Step 5.4.2Simplify the left side.Tap for more steps...Step 5.4.2.1Cancel the common factor of .Tap for more steps...Step 5.4.2.1.1Cancel the common factor.Step 5.4.2.1.2Divide by .Step 5.4.3Simplify the right side.Tap for more steps...Step 5.4.3.1Combine the numerators over the common denominator.Step 5.4.3.2Factor out of .Step 5.4.3.3Factor out of .Step 5.4.3.4Factor out of .Step 5.4.3.5Simplify the expression.Tap for more steps...Step 5.4.3.5.1Rewrite as .Step 5.4.3.5.2Move the negative in front of the fraction.Step 6Replace with .

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