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Product Rule Formula

Product rule help us to differentiate between two or more functions in a given function. If u and v are the given function of x then the Product Rule Formula is given by:

\[\large \frac{d(uv)}{dx}=u\tfrac{dv}{dx}+v\tfrac{du}{dx}\]

When the first function is multiplied by the derivative of the second plus the second function multiplied by the derivative of the first function, then the product rule is given.  Here we take u constant in the first term and v  constant in the second term.

Solved Examples

Question 1: Differentiate the term (x2 + 3)(5x + 4)

Solution:

Given function is (x2 + 3)(5x + 4)

Here u = (x2 + 3) and v = (5x + 4)

$\frac{d((x^2 + 3)(5x + 4))}{dx}$ = ($x^2$ + 3) $\frac{d(5x + 4)}{dx}$ + (5x + 4) $\frac{d(x^2 + 3)}{dx}$

= (x2 + 3) 5 + (5x + 4) 2x

= 5x2 + 15 + 10x + 8x

= 5x2 + 18x + 15.