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Product Rule Calculator
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The product rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

The product rule states that the derivative of the product of two functions is equal to the first times the derivative of the second times the derivative of the first. The constant rule is a special case of the product rule. With these rules we can find the derivatives of rational functions.

In the product rule if f and g both differentiable then 

$\frac{d}{dx}[f(x)g(x)] = f(x)\frac{d}{dx}[g(x)] + g(x)\frac{d}{dx}[f(x)]$
 

Steps for Product Rule Calculator

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Step 1 :  

Read the problem and find the given values.



Step 2 :  

Apply the formula of product rule to find the answers.


$\frac{d}{dx}[f(x)g(x)] = f(x)\frac{d}{dx}[g(x)] + g(x)\frac{d}{dx}[f(x)]$



Problems on Product Rule Calculator

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  1. Using the product rule if f(x) = xex, find f'(x) ?


    Step 1 :  

    Given values


    f(x) = xex



    Step 2 :  

    By applying product rule, we have


    $f'(x) = \frac{d}{dx}(xe^{x}) = x\frac{d}{dx}(e^{x}) + e^{x}\frac{d}{dx}(x)$


    = x.ex + ex.1


    = (x+1)ex



    Answer  :  

    The answer is (x+1)ex



  2. Find the derivative of y = (3x-2x2)(5+4x)?


    Step 1 :  

    Given data


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



    Step 2 :  

    Apply the formula of product rule.


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


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


    = (12x-8x2) + (15-8x-16x2)


    = 15 + 4x - 24x2



    Answer  :  

    The answer is  15 + 4x - 24x2



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