Calculus Examples

Find the Derivative - d/dx 60x(6-x)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
Differentiate.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Add and .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Differentiate using the Power Rule which states that is where .
Step 3.6
Simplify the expression.
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Step 3.6.1
Multiply by .
Step 3.6.2
Move to the left of .
Step 3.6.3
Rewrite as .
Step 3.7
Differentiate using the Power Rule which states that is where .
Step 3.8
Simplify by adding terms.
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Step 3.8.1
Multiply by .
Step 3.8.2
Subtract from .
Step 4
Simplify.
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Step 4.1
Apply the distributive property.
Step 4.2
Combine terms.
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Step 4.2.1
Multiply by .
Step 4.2.2
Multiply by .