Calculus Examples

Find the Derivative - d/dx 3/(x^(1/2))
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Apply basic rules of exponents.
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Step 2.1
Rewrite as .
Step 2.2
Multiply the exponents in .
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Step 2.2.1
Apply the power rule and multiply exponents, .
Step 2.2.2
Combine and .
Step 2.2.3
Move the negative in front of the fraction.
Step 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
Multiply by .
Step 11
Combine and .
Step 12
Simplify the expression.
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Step 12.1
Move to the denominator using the negative exponent rule .
Step 12.2
Move the negative in front of the fraction.