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Find the Derivative - d/dx 5x^2(4+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.

By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Differentiate using the Power Rule which states that is where .
Multiply by .
Differentiate using the Power Rule which states that is where .
Move to the left of .

Step 4
Simplify.

Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Combine terms.

Multiply by .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
Add and .