## 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.