Calculus Examples

Find the Derivative - d/dx ( natural log of x)/(x^7)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Multiply the exponents in .
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Step 2.1
Apply the power rule and multiply exponents, .
Step 2.2
Multiply by .
Step 3
The derivative of with respect to is .
Step 4
Differentiate using the Power Rule.
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Step 4.1
Combine and .
Step 4.2
Cancel the common factor of and .
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Step 4.2.1
Factor out of .
Step 4.2.2
Cancel the common factors.
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Step 4.2.2.1
Raise to the power of .
Step 4.2.2.2
Factor out of .
Step 4.2.2.3
Cancel the common factor.
Step 4.2.2.4
Rewrite the expression.
Step 4.2.2.5
Divide by .
Step 4.3
Differentiate using the Power Rule which states that is where .
Step 4.4
Simplify with factoring out.
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Step 4.4.1
Multiply by .
Step 4.4.2
Factor out of .
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Step 4.4.2.1
Multiply by .
Step 4.4.2.2
Factor out of .
Step 4.4.2.3
Factor out of .
Step 5
Cancel the common factors.
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Step 5.1
Factor out of .
Step 5.2
Cancel the common factor.
Step 5.3
Rewrite the expression.
Step 6
Simplify by moving inside the logarithm.