Calculus Examples

Find the Derivative - d/dx f(x)=4x(5x+3)^4
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 using the chain rule, which states that is where and .
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Step 3.1
To apply the Chain Rule, set as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Replace all occurrences of with .
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
Differentiate using the Power Rule which states that is where .
Step 4.4
Multiply by .
Step 4.5
Since is constant with respect to , the derivative of with respect to is .
Step 4.6
Simplify the expression.
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Step 4.6.1
Add and .
Step 4.6.2
Multiply by .
Step 4.7
Differentiate using the Power Rule which states that is where .
Step 4.8
Multiply by .
Step 5
Simplify.
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Step 5.1
Apply the distributive property.
Step 5.2
Multiply by .
Step 5.3
Factor out of .
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Step 5.3.1
Factor out of .
Step 5.3.2
Factor out of .
Step 5.3.3
Factor out of .
Step 5.4
Add and .