Calculus Examples

Find the Derivative - d/dx x(11-2x)(19-2x)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Add and .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 2.5
Differentiate using the Power Rule which states that is where .
Step 2.6
Simplify the expression.
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Step 2.6.1
Multiply by .
Step 2.6.2
Move to the left of .
Step 3
Differentiate using the Product Rule which states that is where and .
Step 4
Differentiate.
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Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.3
Add and .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 4.5
Differentiate using the Power Rule which states that is where .
Step 4.6
Simplify the expression.
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Step 4.6.1
Multiply by .
Step 4.6.2
Move to the left of .
Step 4.7
Differentiate using the Power Rule which states that is where .
Step 4.8
Simplify by adding terms.
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Step 4.8.1
Multiply by .
Step 4.8.2
Subtract from .
Step 5
Simplify.
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Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Apply the distributive property.
Step 5.4
Apply the distributive property.
Step 5.5
Combine terms.
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Step 5.5.1
Multiply by .
Step 5.5.2
Multiply by .
Step 5.5.3
Raise to the power of .
Step 5.5.4
Raise to the power of .
Step 5.5.5
Use the power rule to combine exponents.
Step 5.5.6
Add and .
Step 5.5.7
Multiply by .
Step 5.5.8
Multiply by .
Step 5.5.9
Raise to the power of .
Step 5.5.10
Raise to the power of .
Step 5.5.11
Use the power rule to combine exponents.
Step 5.5.12
Add and .
Step 5.5.13
Multiply by .
Step 5.5.14
Multiply by .
Step 5.5.15
Subtract from .
Step 5.5.16
Subtract from .
Step 5.5.17
Add and .