Calculus Examples

Differentiate both sides of the equation.
Differentiate the left side of the equation.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Differentiate using the Product Rule which states that is where and .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Remove parentheses around .
Remove parentheses around .
Move to the left of the expression .
Multiply by .
Multiply by .
Evaluate .
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Differentiate using the Product Rule which states that is where and .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Remove parentheses around .
Remove parentheses around .
Move to the left of the expression .
Multiply by .
Remove parentheses around .
Move to the left of the expression .
Multiply by .
Evaluate .
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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 .
Since is constant with respect to , the derivative of with respect to is .
Simplify.
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Remove parentheses.
Add and .
Reorder terms.
Since is constant with respect to , the derivative of with respect to is .
Reform the equation by setting the left side equal to the right side.
Solve for .
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Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Simplify the right side of the equation.
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Simplify terms.
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Combine the numerators over the common denominator.
Simplify each term.
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Simplify the numerator.
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Factor out of .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Apply the distributive property.
Move .
Simplify .
Remove parentheses around .
Simplify each term.
Multiply by .
Simplify with factoring out.
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Factor out of .
Factor out of .
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Rewrite as .
Move .
Multiply by .
Factor out of .
Factor out of .
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Rewrite as .
Move .
Multiply by .
Factor out of .
Simplify the expression.
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Rewrite as .
Reorder terms.
Move the negative in front of the fraction.
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the by cancelling the common factors.
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Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Rewrite the expression.
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Simplify the right side of the equation.
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Multiply the numerator by the reciprocal of the denominator.
Multiply and .
Simplify the expression.
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Remove parentheses around .
Reorder factors in .
Replace with .
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