Calculus Examples

Find the Derivative - d/dx y=1/( natural log of 3x)
Step 1
Rewrite as .
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
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the chain rule, which states that is where and .
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Step 3.1
To apply the Chain Rule, set as .
Step 3.2
The derivative of with respect to is .
Step 3.3
Replace all occurrences of with .
Step 4
Differentiate.
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Step 4.1
Combine and .
Step 4.2
Move to the denominator using the negative exponent rule .
Step 4.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.4
Simplify terms.
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Step 4.4.1
Multiply by .
Step 4.4.2
Combine and .
Step 4.4.3
Cancel the common factor of and .
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Step 4.4.3.1
Factor out of .
Step 4.4.3.2
Cancel the common factors.
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Step 4.4.3.2.1
Factor out of .
Step 4.4.3.2.2
Cancel the common factor.
Step 4.4.3.2.3
Rewrite the expression.
Step 4.4.4
Move the negative in front of the fraction.
Step 4.5
Differentiate using the Power Rule which states that is where .
Step 4.6
Multiply by .