Calculus Examples

Find the Derivative - d/d@VAR f(x)=(e^x)/(3+e^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
Differentiate.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Add and .
Step 4
Differentiate using the Exponential Rule which states that is where =.
Step 5
Multiply by by adding the exponents.
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Step 5.1
Move .
Step 5.2
Use the power rule to combine exponents.
Step 5.3
Add and .
Step 6
Simplify.
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Step 6.1
Apply the distributive property.
Step 6.2
Simplify the numerator.
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Step 6.2.1
Multiply by by adding the exponents.
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Step 6.2.1.1
Use the power rule to combine exponents.
Step 6.2.1.2
Add and .
Step 6.2.2
Combine the opposite terms in .
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Step 6.2.2.1
Subtract from .
Step 6.2.2.2
Add and .