Q:
# What is a derivative of xlnx?

**The derivative of y = xln(x) with respect to x is dy/dx = ln(x) + 1.** This result can be obtained by using the product rule and the well-known results d(ln(x))/dx = 1/x and dx/dx = 1.

The product rule of differentiation states that the derivative of a product of two functions f(x) and g(x) is given by f(x)g'(x) + g(x)f'(x), where f'(x) is the derivative of f(x) with respect to x and g'(x) is the derivative of g(x) with respect to x. Letting f(x) = x and g(x) = ln(x), the mathematician can derive f'(x) = 1 and g'(x) = 1/x. Substituting these values into the formula gives d(xln(x))/dx = ln(x) + 1.

Learn more about Calculus-
Q:
## How do you find the second partial derivative?

A: The second partial derivative for a function with two or more variables is found by differentiating twice in terms of one variable or in terms of one varia... Full Answer >Filed Under: -
Q:
## What is the derivative of sin squared?

A: The derivative of sine squared is the sine of 2x, expressed as d/dx (sin2(x)) = sin(2x). The derivative function describes the slope of a line at a given p... Full Answer >Filed Under: -
Q:
## How do you explain a gradient vector field in calculus?

A: Lamar University explains that a gradient vector field is a directional derivative that represents the change in the gradient of a function. Gradient field... Full Answer >Filed Under: -
Q:
## What is instantaneous velocity in calculus?

A: The instantaneous velocity in calculus is the first derivative of a function that expresses distance as a function of time. The instantaneous velocity is a... Full Answer >Filed Under: