Calculus Examples

Find the Derivative - d/dx y = natural log of 10/x
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
Multiply by the reciprocal of the fraction to divide by .
Step 3
Multiply by .
Step 4
Since is constant with respect to , the derivative of with respect to is .
Step 5
Simplify terms.
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Step 5.1
Combine and .
Step 5.2
Cancel the common factor of .
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Step 5.2.1
Cancel the common factor.
Step 5.2.2
Divide by .
Step 5.3
Rewrite as .
Step 6
Differentiate using the Power Rule which states that is where .
Step 7
Raise to the power of .
Step 8
Use the power rule to combine exponents.
Step 9
Subtract from .
Step 10
Rewrite the expression using the negative exponent rule .