Calculus Examples

Find the Derivative - d/dx (e^x)/(8x^2)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Multiply the exponents in .
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Step 3.1
Apply the power rule and multiply exponents, .
Step 3.2
Multiply by .
Step 4
Differentiate using the Exponential Rule which states that is where =.
Step 5
Differentiate using the Power Rule.
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Step 5.1
Differentiate using the Power Rule which states that is where .
Step 5.2
Combine fractions.
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Step 5.2.1
Multiply by .
Step 5.2.2
Multiply by .
Step 6
Simplify.
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Step 6.1
Reorder factors in .
Step 6.2
Reorder terms.
Step 6.3
Simplify the numerator.
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Step 6.3.1
Factor out of .
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Step 6.3.1.1
Factor out of .
Step 6.3.1.2
Factor out of .
Step 6.3.1.3
Factor out of .
Step 6.3.2
Factor out of .
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Step 6.3.2.1
Factor out of .
Step 6.3.2.2
Factor out of .
Step 6.3.2.3
Factor out of .
Step 6.4
Cancel the common factor of and .
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Step 6.4.1
Factor out of .
Step 6.4.2
Cancel the common factors.
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Step 6.4.2.1
Factor out of .
Step 6.4.2.2
Cancel the common factor.
Step 6.4.2.3
Rewrite the expression.