Calculus Examples

Find the Derivative - d/d@VAR f(x)=( square root of natural log of x)/x
Step 1
Use to rewrite as .
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
Differentiate using the Power Rule which states that is where .
Step 3.3
Replace all occurrences of with .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Simplify the numerator.
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Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Combine fractions.
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Step 8.1
Move the negative in front of the fraction.
Step 8.2
Combine and .
Step 8.3
Move to the denominator using the negative exponent rule .
Step 8.4
Combine and .
Step 9
The derivative of with respect to is .
Step 10
Simplify terms.
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Step 10.1
Multiply by .
Step 10.2
Cancel the common factor.
Step 10.3
Rewrite the expression.
Step 11
Multiply by .
Step 12
Combine.
Step 13
Apply the distributive property.
Step 14
Cancel the common factor of .
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Step 14.1
Cancel the common factor.
Step 14.2
Rewrite the expression.
Step 15
Multiply by .
Step 16
Use the power rule to combine exponents.
Step 17
Simplify the expression.
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Step 17.1
Combine the numerators over the common denominator.
Step 17.2
Add and .
Step 18
Cancel the common factor of .
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Step 18.1
Cancel the common factor.
Step 18.2
Rewrite the expression.
Step 19
Simplify.
Step 20
Differentiate using the Power Rule which states that is where .
Step 21
Multiply by .
Step 22
Simplify.
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Step 22.1
Simplify by moving inside the logarithm.
Step 22.2
Reorder terms.