Implicit and Logarithmic Differentiation

These flashcards cover key terms and concepts related to implicit and logarithmic differentiation, essential for calculus.

Implicit Differentiation

A method used to find derivatives of functions that are not explicitly solved for one variable in terms of another.

Logarithmic Rule

A rule used in differentiation that involves the logarithm of a function, often using the product or chain rule.

f'(x) = x' ln x + x (en x)' = ln x + 1

The derivative of the function f(x) = x ln x, calculated using the product rule.

Derivative of ln x

If y = ln x, then dy/dx = 1/x, valid for x > 0.

Chain Rule

A formula for computing the derivative of the composition of two or more functions.

Logarithmic Differentiation

A technique used to differentiate functions that are products or quotients by taking the logarithm of both sides.

Domain of f(x) = ln x

The domain is (0, ∞) since the natural logarithm is only defined for positive x.

dy/dx

Symbol denoting the derivative of y with respect to x.