Final answer:
The chain rule calculator helps find derivatives of composite functions, the Jacobian matrix calculator is used to represent derivatives of vector-valued functions, and the directional derivative calculator measures the rate of change of a function along a specified direction.
Step-by-step explanation:
Chain Rule Calculator:
The chain rule is a useful tool in calculus for finding the derivative of a composition of functions. To calculate the derivative using the chain rule, you need to identify the inner function and the outer function. Then, apply the chain rule formula, which states that the derivative of the composition function is equal to the derivative of the outer function multiplied by the derivative of the inner function.
Jacobian Matrix Calculator:
The Jacobian matrix is used in multivariable calculus to represent the derivatives of a vector-valued function with respect to its variables. To calculate the Jacobian matrix, you need to find the partial derivatives of each component function and arrange them in a matrix. The resulting matrix represents the rate of change of each component function with respect to its variables.
Directional Derivative Calculator:
The directional derivative measures the rate at which a function changes along a specified direction. To calculate the directional derivative, you need to find the gradient of the function and then take the dot product with the direction vector. The result represents the rate of change of the function in that direction.