Calculus Examples

Find dy/dx y = natural log of square root of x
Step 1
Use to rewrite as .
Step 2
Differentiate both sides of the equation.
Step 3
The derivative of with respect to is .
Step 4
Differentiate the right side of the equation.
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Step 4.1
Differentiate using the chain rule, which states that is where and .
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Step 4.1.1
To apply the Chain Rule, set as .
Step 4.1.2
The derivative of with respect to is .
Step 4.1.3
Replace all occurrences of with .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
To write as a fraction with a common denominator, multiply by .
Step 4.4
Combine and .
Step 4.5
Combine the numerators over the common denominator.
Step 4.6
Simplify the numerator.
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Step 4.6.1
Multiply by .
Step 4.6.2
Subtract from .
Step 4.7
Move the negative in front of the fraction.
Step 4.8
Combine and .
Step 4.9
Multiply by .
Step 4.10
Simplify the expression.
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Step 4.10.1
Move to the left of .
Step 4.10.2
Move to the denominator using the negative exponent rule .
Step 4.11
Simplify the denominator.
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Step 4.11.1
Multiply by by adding the exponents.
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Step 4.11.1.1
Move .
Step 4.11.1.2
Use the power rule to combine exponents.
Step 4.11.1.3
Combine the numerators over the common denominator.
Step 4.11.1.4
Add and .
Step 4.11.1.5
Divide by .
Step 4.11.2
Simplify .
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Replace with .