# What is a product rule?

## What is a product rule?

Example FAQs Product Rule Definition The product rule is a general rule for the problems which come under the differentiation where one function is multiplied by another function.

## What is the derivative of a function using the product rule?

DIFFERENTIATION USING THE PRODUCT RULE The following problems require the use of the product rule. In the following discussion and solutions the derivative of a function h(x) will be denoted by or h'(x) . The product rule is a formal rule for differentiating problems where one function is multiplied by another.

How do you find the product rule of differentiation?

Product Rule Formula If we have a function y = uv, where u and v are the functions of x. Then, by the use of the product rule, we can easily find out the derivative of y with respect to x, and can be written as: (dy/dx) = u (dv/dx) + v (du/dx) The above formula is called the product rule for derivativesor the product rule of differentiation.

### What is the product rule for exponents?

Product Rule for Exponent: If m and n are the natural numbers, then xn× xm = xn+m. Product rule cannot be used to solve expression of exponent having a different base like 23* 54and expressions like (xn)m. An expression like (xn)mcan be solved only with the help of Power Rule of Exponents where (xn)m= xnm.

### Does the product rule apply to gradients?

Yes, the product rule as you have written it applies to gradients. This is easy to see by evaluating ∇ ( f g) in a Cartesian system, where (3) ∇ ( f g) = g ∇ f + f ∇ g. Show activity on this post.

What is the product rule for differentiable functions?

Product rule states that when two functions f(x) and g(x) are differentiable, then their product is also differentiable and is calculated using the formula, (fg)'(x) = f(x) g'(x) + f'(x) g(x)

## What is the product rule for derivatives and exponents?

Product Rule for Derivatives: For any two functions, say f(x) and g(x), the product rule is D [f(x) g(x)] = f(x) D[g(x)] + g(x) D[f(x)] d(uv)/dx = u(dv/dx)+ v(du/dx) where u and v are two functions Product Rule for Exponent: If m and n are the natural numbers, then xn× xm = xn+m.