Trigonometry Examples

Find the Derivative - d/dx (arctan(5/x))
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
Differentiate.
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Since is constant with respect to , the derivative of with respect to is .
Combine fractions.
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Combine and .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Combine fractions.
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Combine and .
Move to the denominator using the negative exponent rule .
Simplify.
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Apply the product rule to .
Apply the distributive property.
Combine terms.
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Multiply by .
Raise to the power of .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
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