Differentiate y = x(x+3)^4
To differentiate this function we use the product rule. In the product rule we, leave the first alone, differentiate the second, and leave the second alone, differentiate the first. Say y = U * V (U and V are both functions of x) Then in general we have y' = U dV/dx + V dU/dx For this example we have; y' = x * d/dx (x+3)4 + (x+3)4 d/dx x y' = x * 4 * (x+3)3 * 1 + (x+3)4 * 1 When differentiating bracketed term we start differentiating outside the brackets and work our way in, therefore initially treating the brackets like a single term then accounting for the terms inside the brackets. To simplify the final expression we now take out the common factor. y' = (x+3)3 [4x + (x+3)] Therefore, y' = (x+3)3 (5x+3)
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