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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Differentiate both sides of the equation.
Step 3
The derivative of with respect to is .
Step 4
Step 4.1
Differentiate using the Product Rule which states that is where and .
Step 4.2
Differentiate using the Power Rule.
Step 4.2.1
Rewrite as .
Step 4.2.2
Multiply the exponents in .
Step 4.2.2.1
Apply the power rule and multiply exponents, .
Step 4.2.2.2
Combine and .
Step 4.2.2.3
Move the negative in front of the fraction.
Step 4.2.3
Differentiate using the Power Rule which states that is where .
Step 4.3
To write as a fraction with a common denominator, multiply by .
Step 4.4
Combine and .
Step 4.5
Combine the numerators over the common denominator.
Step 4.6
Simplify the numerator.
Step 4.6.1
Multiply by .
Step 4.6.2
Subtract from .
Step 4.7
Combine fractions.
Step 4.7.1
Move the negative in front of the fraction.
Step 4.7.2
Combine and .
Step 4.7.3
Simplify the expression.
Step 4.7.3.1
Multiply by .
Step 4.7.3.2
Multiply by .
Step 4.7.3.3
Move to the denominator using the negative exponent rule .
Step 4.8
Since is constant with respect to , the derivative of with respect to is .
Step 4.9
Simplify the expression.
Step 4.9.1
Multiply by .
Step 4.9.2
Add and .
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Replace with .