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A piecewise function is usually defined by more than one formula: a fomula for each interval. Example 1: f( x ) = - x if x <= 2 = x if x > 2 What the above says is that if x is smaller than or equal to 2, the formula for the function is f( x ) = -x and if x is greater than 2, the formula is f( x ) = x.
To demonstrate, we would use the quotient rule if we had a fraction in our function with variables in both the numerator and denominator of the fraction. For example, if. To find f'(x), we would need to use the quotient rule.Quotient Rule: =. so we write as g(x)/h(x), where g(x) = 3x 2 + 4x - 5, and h(x) = e x + x 2. Then we know that g'(x) = 6x + 4, and h'(x) = e x + 2x. Then. The gut impulse for many students is to use the quotient rule whenever there is a fraction in our expression.n order to differentiate this, we need the product rule. The product rule allows us to differentiate a function when the function is a product of two distinct parts. In this example, we have the polynomial 3x 2 + 4x - 5 and the transcendental function sin(x).