Calculus Examples

Find the Derivative - d/dx f(x)=|x^2-25|
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Combine fractions.
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Step 2.4.1
Add and .
Step 2.4.2
Combine and .
Step 2.4.3
Combine and .
Step 3
Simplify.
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Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Simplify each term.
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Step 3.3.1
Multiply by by adding the exponents.
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Step 3.3.1.1
Move .
Step 3.3.1.2
Multiply by .
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Step 3.3.1.2.1
Raise to the power of .
Step 3.3.1.2.2
Use the power rule to combine exponents.
Step 3.3.1.3
Add and .
Step 3.3.2
Multiply by .