Calculus Examples

Find the Derivative - d/dx (arcsin(3x))/x
Step 1
Differentiate using the Quotient 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 3.2.1.3
Multiply by .
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 4
Multiply by .
Step 5
Simplify terms.
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Step 5.1
Combine.
Step 5.2
Apply the distributive property.
Step 5.3
Cancel the common factor of .
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Step 5.3.1
Cancel the common factor.
Step 5.3.2
Rewrite the expression.
Step 6
Differentiate using the Power Rule which states that is where .
Step 7
Multiply by .
Step 8
Simplify.
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Step 8.1
Simplify each term.
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Step 8.1.1
Rewrite using the commutative property of multiplication.
Step 8.1.2
Rewrite as .
Step 8.1.3
Rewrite as .
Step 8.1.4
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 8.1.5
Multiply by .
Step 8.2
Reorder terms.