Calculus Examples

Find the Derivative - d/dx y=p^( square root of x)
Step 1
Use to rewrite as .
Step 2
Differentiate using the Generalized Power Rule which states that is where and .
Step 3
Differentiate.
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Simplify the expression.
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Step 3.2.1
Multiply by .
Step 3.2.2
Multiply by .
Step 3.2.3
Add and .
Step 3.3
Differentiate using the Power Rule which states that is where .
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
Move the negative in front of the fraction.
Step 9
Combine and .
Step 10
Combine and .
Step 11
Combine and .
Step 12
Move to the denominator using the negative exponent rule .