Explain Product Rule Explain Product Rule Product rule means product of two or more function. Suppose we have two function first function f(x), and second function g(x) then we can defined its product as: d/dx(f(x) g(x)) = g(x)d/dx (f(x)) + f(x)d/dx (g(x)), Or, f(x) g(x) = f’(x) g(x) + f(x) g’(x).Let’s see few examples in order to understand the concept. Example 1: Differentiate the given function by product rule where y = x2? Solution: Step 1: First we would write the function,y = x * x,First function:f(x) = x,Second function: g(x) = x, Step 2: In this step we would differentiate the given function with respect to 'x',By product rule: d/dx (f(x)g(x))= g(x)d/dx (f(x)) + f(x) d/dx (g(x)),dy/dx = (x) d/dx (x) + (x) d/dx (x),d/dx (y) = x *1 + 1*x, d/dx (y) = 2x, Example2: Differentiate the given function by product rule where y = (x+1) (x+2)? Know More About Multiply 1/2 and -1/4

Solution: Step 1: First we would write the function,y = (x +1)*(x+2),First function:f(x) = (x+1), Second function: g(x) = (x+2), Step 2: In this step we would differentiate the given function with respect to x,By product rule: d/dx (f(x) g(x)) = g(x) d/dx (f(x)) + f(x) d/dx (g(x)), dy/dx = (x+2) d/dx (x+1) + (x+1) d/dx (x+2), d/dx (y) = (x +2)*1 + 1*(x+1), d/dx (y) = 2x +3, Example 3: Differentiate the given function by product rule where y = (x2+2) (x3+4)? Solution: step 1: First we would write the function,y = (x2+2) (x3+4),First function: f(x) = (x2+2),Second function: g(x) = (x3+4), Step 2: In this step we would differentiate the given function with respect to x, By product rule: d/dx (f(x) g(x)) = g(x) d/dx (f(x)) + f(x) d/dx (g(x)),dy/dx = (x3+4) d/dx (x2+2) + (x2+2) d/dx (x4+4),d/dx (y) = (x3 +4) *2x + (x2+2) *4x3, d/dx (y) = 2x4 +8x + 4x5 +8x3. d/dx (y) = 4x5 + 2x4 +8x3 +8x This is all about product rule.

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