Calculus Examples

Find the Derivative - d/d@VAR f(x)=(x+(x)^(1/2))^(1/2)
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
Differentiate using the Power Rule which states that is where .
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
Combine and .
Step 4
Combine the numerators over the common denominator.
Step 5
Simplify the numerator.
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Step 5.1
Multiply by .
Step 5.2
Subtract from .
Step 6
Combine fractions.
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Step 6.1
Move the negative in front of the fraction.
Step 6.2
Combine and .
Step 6.3
Move to the denominator using the negative exponent rule .
Step 7
By the Sum Rule, the derivative of with respect to is .
Step 8
Differentiate using the Power Rule which states that is where .
Step 9
Differentiate using the Power Rule which states that is where .
Step 10
To write as a fraction with a common denominator, multiply by .
Step 11
Combine and .
Step 12
Combine the numerators over the common denominator.
Step 13
Simplify the numerator.
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Step 13.1
Multiply by .
Step 13.2
Subtract from .
Step 14
Move the negative in front of the fraction.
Step 15
Combine and .
Step 16
Move to the denominator using the negative exponent rule .
Step 17
Simplify.
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Step 17.1
Reorder the factors of .
Step 17.2
Multiply by .
Step 17.3
Simplify the numerator.
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Step 17.3.1
Write as a fraction with a common denominator.
Step 17.3.2
Combine the numerators over the common denominator.
Step 17.4
Multiply the numerator by the reciprocal of the denominator.
Step 17.5
Multiply .
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Step 17.5.1
Multiply by .
Step 17.5.2
Multiply by .