Calculus Examples

Find the Derivative - d/dx y=(2e^x)/(x^2+6)
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
Differentiate using the Exponential Rule which states that is where =.
Step 4
Differentiate.
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Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.4
Combine fractions.
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Step 4.4.1
Add and .
Step 4.4.2
Multiply by .
Step 4.4.3
Combine and .
Step 5
Simplify.
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Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Simplify the numerator.
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Step 5.3.1
Simplify each term.
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Step 5.3.1.1
Multiply by .
Step 5.3.1.2
Multiply by .
Step 5.3.2
Reorder factors in .
Step 5.4
Reorder terms.
Step 5.5
Factor out of .
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Step 5.5.1
Factor out of .
Step 5.5.2
Factor out of .
Step 5.5.3
Factor out of .
Step 5.5.4
Factor out of .
Step 5.5.5
Factor out of .