Calculus Examples

Find the Derivative - d/dx y = natural log of 8-3x
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
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Add and .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 2.5
Combine fractions.
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Step 2.5.1
Combine and .
Step 2.5.2
Move the negative in front of the fraction.
Step 2.6
Differentiate using the Power Rule which states that is where .
Step 2.7
Multiply by .