Calculus Examples

Find the Derivative - d/dx (e^x)/( natural log of x)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate using the Exponential Rule which states that is where =.
Step 3
The derivative of with respect to is .
Step 4
Combine and .
Step 5
Simplify.
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Step 5.1
Reorder factors in .
Step 5.2
Simplify the numerator.
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Step 5.2.1
Factor out of .
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Step 5.2.1.1
Factor out of .
Step 5.2.1.2
Factor out of .
Step 5.2.1.3
Factor out of .
Step 5.2.2
To write as a fraction with a common denominator, multiply by .
Step 5.2.3
Combine the numerators over the common denominator.
Step 5.3
Combine and .
Step 5.4
Multiply the numerator by the reciprocal of the denominator.
Step 5.5
Combine.
Step 5.6
Multiply by .
Step 5.7
Reorder factors in .