I don't understand what you are asking. You ask about finding the derivative but then give the derivative. Are asking for the partial derivatives of ex+y and 1/(ex+ ey or are you saying these are the derivatives and you want to find z?nicolette2413 said:
It is always a good idea to state the entire problem!nicolette2413 said:
The derivative of exey with respect to x is just exey again and I think you have that in your answer. But the derivative of ex+ ey is just ex because ey is a constant with respect to x and its derivative is 0.
A partial derivative of natural log is a mathematical concept used in multivariate calculus to measure the rate of change of a function with respect to one of its variables while holding other variables constant. It is denoted by ∂ln(f)/∂x, where f is the function and x is the variable of interest.
To calculate a partial derivative of natural log, you need to apply the chain rule. First, take the derivative of the natural log function, which is 1/x. Then, multiply it by the derivative of the inner function with respect to the variable of interest. Finally, simplify the expression if possible.
Partial derivatives of natural log have various applications in real life, such as in economics, physics, and engineering. They are used to optimize functions and find the maximum or minimum values, which can be useful in decision-making processes and problem-solving.
Yes, partial derivatives of natural log can be negative. This indicates a decreasing rate of change of the function with respect to the variable of interest. Similarly, a positive partial derivative indicates an increasing rate of change.
One limitation of using partial derivatives of natural log is that they only measure the rate of change of a function in one direction. They do not provide information about the overall behavior of the function. Additionally, they can only be used for differentiable functions.