Calculus Examples

Find the Derivative - d/dx natural log of x^0.5
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate using the Power Rule.
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Step 2.1
Differentiate using the Power Rule which states that is where .
Step 2.2
Combine fractions.
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Step 2.2.1
Combine and .
Step 2.2.2
Combine and .
Step 2.2.3
Move to the denominator using the negative exponent rule .
Step 3
Simplify the denominator.
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Step 3.1
Multiply by by adding the exponents.
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Step 3.1.1
Use the power rule to combine exponents.
Step 3.1.2
Add and .
Step 3.2
Simplify .