Calculus Examples

Find the Derivative - d/du g(u) = square root of 3u+ square root of 5u
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Multiply by .
Step 3
Evaluate .
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Step 3.1
Use to rewrite as .
Step 3.2
Factor out of .
Step 3.3
Apply the product rule to .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Differentiate using the Power Rule which states that is where .
Step 3.6
To write as a fraction with a common denominator, multiply by .
Step 3.7
Combine and .
Step 3.8
Combine the numerators over the common denominator.
Step 3.9
Simplify the numerator.
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Step 3.9.1
Multiply by .
Step 3.9.2
Subtract from .
Step 3.10
Move the negative in front of the fraction.
Step 3.11
Combine and .
Step 3.12
Combine and .
Step 3.13
Move to the denominator using the negative exponent rule .
Step 4
Reorder terms.