Calculus Examples

Find the Derivative - d/dx arctan(30/x)
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate.
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Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Combine fractions.
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Step 2.2.1
Combine and .
Step 2.2.2
Rewrite as .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Combine fractions.
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Step 2.4.1
Combine and .
Step 2.4.2
Move to the denominator using the negative exponent rule .
Step 3
Simplify.
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Step 3.1
Apply the product rule to .
Step 3.2
Apply the distributive property.
Step 3.3
Combine terms.
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Step 3.3.1
Multiply by .
Step 3.3.2
Raise to the power of .
Step 3.3.3
Combine and .
Step 3.3.4
Cancel the common factor of .
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Step 3.3.4.1
Cancel the common factor.
Step 3.3.4.2
Divide by .