Calculus Examples

Find the Derivative - d/dx (x^5-5x)/5
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
By the Sum Rule, the derivative of with respect to is .
Step 3
Differentiate using the Power Rule which states that is where .
Step 4
Since is constant with respect to , the derivative of with respect to is .
Step 5
Differentiate using the Power Rule which states that is where .
Step 6
Multiply by .
Step 7
Simplify.
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Step 7.1
Apply the distributive property.
Step 7.2
Combine terms.
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Step 7.2.1
Combine and .
Step 7.2.2
Combine and .
Step 7.2.3
Cancel the common factor of .
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Step 7.2.3.1
Cancel the common factor.
Step 7.2.3.2
Divide by .
Step 7.2.4
Combine and .
Step 7.2.5
Cancel the common factor of and .
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Step 7.2.5.1
Factor out of .
Step 7.2.5.2
Cancel the common factors.
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Step 7.2.5.2.1
Factor out of .
Step 7.2.5.2.2
Cancel the common factor.
Step 7.2.5.2.3
Rewrite the expression.
Step 7.2.5.2.4
Divide by .