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Calculus Examples
Step 1
Step 1.1
Since is constant with respect to , the derivative of with respect to is .
Step 1.2
Differentiate using the Power Rule which states that is where .
Step 1.3
To write as a fraction with a common denominator, multiply by .
Step 1.4
Combine and .
Step 1.5
Combine the numerators over the common denominator.
Step 1.6
Simplify the numerator.
Step 1.6.1
Multiply by .
Step 1.6.2
Subtract from .
Step 1.7
Combine and .
Step 1.8
Combine and .
Step 1.9
Multiply by .
Step 2
Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
To write as a fraction with a common denominator, multiply by .
Step 2.4
Combine and .
Step 2.5
Combine the numerators over the common denominator.
Step 2.6
Simplify the numerator.
Step 2.6.1
Multiply by .
Step 2.6.2
Subtract from .
Step 2.7
Move the negative in front of the fraction.
Step 2.8
Combine and .
Step 2.9
Multiply by .
Step 2.10
Multiply.
Step 2.10.1
Multiply by .
Step 2.10.2
Move to the denominator using the negative exponent rule .
Step 3
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Apply basic rules of exponents.
Step 3.2.1
Rewrite as .
Step 3.2.2
Multiply the exponents in .
Step 3.2.2.1
Apply the power rule and multiply exponents, .
Step 3.2.2.2
Combine and .
Step 3.2.2.3
Move the negative in front of the fraction.
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
To write as a fraction with a common denominator, multiply by .
Step 3.5
Combine and .
Step 3.6
Combine the numerators over the common denominator.
Step 3.7
Simplify the numerator.
Step 3.7.1
Multiply by .
Step 3.7.2
Subtract from .
Step 3.8
Move the negative in front of the fraction.
Step 3.9
Combine and .
Step 3.10
Multiply by .
Step 3.11
Multiply.
Step 3.11.1
Multiply by .
Step 3.11.2
Move to the denominator using the negative exponent rule .
Step 4
Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Apply basic rules of exponents.
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
Multiply .
Step 4.2.2.2.1
Combine and .
Step 4.2.2.2.2
Multiply by .
Step 4.2.2.3
Move the negative in front of the fraction.
Step 4.3
Differentiate using the Power Rule which states that is where .
Step 4.4
To write as a fraction with a common denominator, multiply by .
Step 4.5
Combine and .
Step 4.6
Combine the numerators over the common denominator.
Step 4.7
Simplify the numerator.
Step 4.7.1
Multiply by .
Step 4.7.2
Subtract from .
Step 4.8
Move the negative in front of the fraction.
Step 4.9
Combine and .
Step 4.10
Multiply.
Step 4.10.1
Multiply by .
Step 4.10.2
Multiply by .
Step 4.11
Multiply by .
Step 4.12
Multiply.
Step 4.12.1
Multiply by .
Step 4.12.2
Multiply by .
Step 4.12.3
Move to the denominator using the negative exponent rule .
Step 5
The fourth derivative of with respect to is .