| Term | Definition |
|---|---|
| chain rule | A differentiation rule that provides a method for finding the derivative of a composite function by multiplying the derivative of the outer function by the derivative of the inner function. |
| composite function | A function formed by combining two functions where the output of one function becomes the input of another. |
| derivative | The instantaneous rate of change of a function at a specific point, representing the slope of the tangent line to the function at that point. |
| differentiable function | Functions that have a derivative at every point in their domain, meaning they are smooth and continuous without sharp corners or breaks. |
| Term | Definition |
|---|---|
| chain rule | A differentiation rule that provides a method for finding the derivative of a composite function by multiplying the derivative of the outer function by the derivative of the inner function. |
| derivative | The instantaneous rate of change of a function at a specific point, representing the slope of the tangent line to the function at that point. |
| implicit differentiation | A technique for finding the derivative of a function defined implicitly by differentiating both sides of an equation with respect to the independent variable. |
| implicitly defined function | A function defined by an equation relating x and y, where y is not explicitly solved in terms of x. |
| Term | Definition |
|---|---|
| chain rule | A differentiation rule that provides a method for finding the derivative of a composite function by multiplying the derivative of the outer function by the derivative of the inner function. |
| derivative | The instantaneous rate of change of a function at a specific point, representing the slope of the tangent line to the function at that point. |
| inverse function | A function that reverses the effect of another function, such that if f(a) = b, then the inverse function f⁻¹(b) = a. |
| inverse trigonometric functions | Functions that reverse the action of trigonometric functions, such as arcsine, arccosine, and arctangent, which return an angle given a trigonometric ratio. |
| Term | Definition |
|---|---|
| chain rule | A differentiation rule that provides a method for finding the derivative of a composite function by multiplying the derivative of the outer function by the derivative of the inner function. |
| derivative | The instantaneous rate of change of a function at a specific point, representing the slope of the tangent line to the function at that point. |
| inverse function | A function that reverses the effect of another function, such that if f(a) = b, then the inverse function f⁻¹(b) = a. |
| inverse trigonometric functions | Functions that reverse the action of trigonometric functions, such as arcsine, arccosine, and arctangent, which return an angle given a trigonometric ratio. |
| Term | Definition |
|---|---|
| first derivative | The derivative of a function, denoted f', which describes the rate of change and indicates where a function is increasing or decreasing. |
| higher-order derivatives | Derivatives of derivatives obtained by repeatedly differentiating a function; the second derivative, third derivative, and beyond. |
| second derivative | The derivative of the first derivative, denoted f'', which describes the concavity of a function and indicates where it is concave up or concave down. |