Calculus Examples

Find the Derivative - d/dx x^2arctan(9x)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate.
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Step 3.1
Factor out of .
Step 3.2
Combine fractions.
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Step 3.2.1
Simplify the expression.
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Step 3.2.1.1
Apply the product rule to .
Step 3.2.1.2
Raise to the power of .
Step 3.2.2
Combine and .
Step 3.3
Since is constant with respect to , the derivative of with respect to is .
Step 3.4
Combine and .
Step 3.5
Differentiate using the Power Rule which states that is where .
Step 3.6
Multiply by .
Step 3.7
Differentiate using the Power Rule which states that is where .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify.
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Step 6.1
Apply the distributive property.
Step 6.2
Simplify the numerator.
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Step 6.2.1
Simplify each term.
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Step 6.2.1.1
Rewrite using the commutative property of multiplication.
Step 6.2.1.2
Multiply by .
Step 6.2.1.3
Multiply by by adding the exponents.
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Step 6.2.1.3.1
Move .
Step 6.2.1.3.2
Multiply by .
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Step 6.2.1.3.2.1
Raise to the power of .
Step 6.2.1.3.2.2
Use the power rule to combine exponents.
Step 6.2.1.3.3
Add and .
Step 6.2.1.4
Rewrite using the commutative property of multiplication.
Step 6.2.1.5
Multiply by .
Step 6.2.2
Reorder factors in .
Step 6.3
Reorder terms.