Calculus Examples

Find the Derivative - d/dx x(2x-3)^(1/2)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Combine and .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify the numerator.
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Step 6.1
Multiply by .
Step 6.2
Subtract from .
Step 7
Combine fractions.
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Step 7.1
Move the negative in front of the fraction.
Step 7.2
Combine and .
Step 7.3
Move to the denominator using the negative exponent rule .
Step 7.4
Combine and .
Step 8
By the Sum Rule, the derivative of with respect to is .
Step 9
Since is constant with respect to , the derivative of with respect to is .
Step 10
Differentiate using the Power Rule which states that is where .
Step 11
Multiply by .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Simplify terms.
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Step 13.1
Add and .
Step 13.2
Combine and .
Step 13.3
Move to the left of .
Step 13.4
Cancel the common factor.
Step 13.5
Rewrite the expression.
Step 14
Differentiate using the Power Rule which states that is where .
Step 15
Multiply by .
Step 16
To write as a fraction with a common denominator, multiply by .
Step 17
Combine the numerators over the common denominator.
Step 18
Multiply by by adding the exponents.
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Step 18.1
Use the power rule to combine exponents.
Step 18.2
Combine the numerators over the common denominator.
Step 18.3
Add and .
Step 18.4
Divide by .
Step 19
Simplify .
Step 20
Add and .