Calculus Examples

Find dV/dr V=4/3*(pr^3)
Step 1
Remove parentheses.
Step 2
Differentiate both sides of the equation.
Step 3
The derivative of with respect to is .
Step 4
Differentiate the right side of the equation.
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Step 4.1
Combine fractions.
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Step 4.1.1
Combine and .
Step 4.1.2
Combine and .
Step 4.1.3
Move to the left of .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.3
Differentiate using the Power Rule which states that is where .
Step 4.4
Simplify terms.
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Step 4.4.1
Combine and .
Step 4.4.2
Multiply by .
Step 4.4.3
Combine and .
Step 4.4.4
Cancel the common factor of and .
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Step 4.4.4.1
Factor out of .
Step 4.4.4.2
Cancel the common factors.
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Step 4.4.4.2.1
Factor out of .
Step 4.4.4.2.2
Cancel the common factor.
Step 4.4.4.2.3
Rewrite the expression.
Step 4.4.4.2.4
Divide by .
Step 4.4.5
Reorder the factors of .
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Replace with .