# Find the Derivative f(x) = natural log of x+4+(e^(-3x))

Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Differentiate.
Since is constant with respect to , the derivative of with respect to is .
Move to the left of .
Differentiate using the Power Rule which states that is where .
Simplify the expression.
Multiply by .
Reorder the factors of .
Find the Derivative f(x) = natural log of x+4+(e^(-3x))

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