Calculus Examples

Find the Derivative - d/dx square root of x natural log of x
Step 1
Use to rewrite as .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Combine fractions.
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Step 4.1
Combine and .
Step 4.2
Move to the denominator using the negative exponent rule .
Step 5
Multiply by by adding the exponents.
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Step 5.1
Multiply by .
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Step 5.1.1
Raise to the power of .
Step 5.1.2
Use the power rule to combine exponents.
Step 5.2
Write as a fraction with a common denominator.
Step 5.3
Combine the numerators over the common denominator.
Step 5.4
Subtract from .
Step 6
Differentiate using the Power Rule which states that is where .
Step 7
To write as a fraction with a common denominator, multiply by .
Step 8
Combine and .
Step 9
Combine the numerators over the common denominator.
Step 10
Simplify the numerator.
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Step 10.1
Multiply by .
Step 10.2
Subtract from .
Step 11
Move the negative in front of the fraction.
Step 12
Combine and .
Step 13
Combine and .
Step 14
Move to the denominator using the negative exponent rule .