Exponential and Logarithmic Derivatives

Definition

Exponential and logarithmic derivatives are rules used to find the derivative of functions involving exponential or logarithmic functions. The exponential rule states that the derivative of an exponential function is equal to the original function multiplied by its natural logarithm base, while the logarithmic rule states that the derivative of a logarithmic function is equal to the reciprocal of the original function.

Related terms

Product Rule:

The product rule is used to find the derivative of a product of two functions. It states that when differentiating a product, you take the derivative of one function times the other function plus vice versa.

Quotient Rule:

The quotient rule is used to find the derivative of a quotient (division) between two functions. It states that when differentiating a quotient, you take the denominator times its derivative minus numerator times its derivative divided by denominator squared.

Chain Rule:

The chain rule is used to find derivatives when there are compositions (functions within functions). It states that when differentiating a composition, you multiply together derivatives at each level and apply them sequentially from inside out.