Calculus Examples

Find the Derivative - d/dx ( natural log of 5x)/(5x)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
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
Cancel the common factor of .
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Step 4.2.1
Cancel the common factor.
Step 4.2.2
Rewrite the expression.
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
Combine and .
Step 4.4.2
Cancel the common factor of .
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Step 4.4.2.1
Cancel the common factor.
Step 4.4.2.2
Rewrite the expression.
Step 4.4.3
Multiply by .
Step 4.5
Differentiate using the Power Rule which states that is where .
Step 4.6
Differentiate using the Power Rule which states that is where .
Step 4.7
Combine fractions.
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Step 4.7.1
Multiply by .
Step 4.7.2
Multiply by .