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:
## What is the derivative of 3x?

A: The derivative of 3x is 3. Whenever a mathematical function is defined by a constant multiplied by x, the derivative of the function equals the constant. T... Full Answer >Filed Under: -
Q:
## What is the significance of ln 1/x in calculus?

A: In calculus, the primary significance of 1/x is its value as the derivative of the natural logarithm of "x." The proof for the derivative of ln(x) may be f... Full Answer >Filed Under: -
Q:
## What is the derivative of the square root of x?

A: The derivative of the square root of x is one-half times one divided by the square root of x. The square root of x is equal to x to the power of one-half. Full Answer >Filed Under: -
Q:
## What is logarithmic differentiation?

A: Logarithmic differentiation refers to the process in calculus of finding the derivative of a function by using the properties of the natural logarithmic fu... Full Answer >Filed Under: