Finding derivative of a product

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I am wondering if there is a way to find the derivative of the following without multiplying the whole thing out and then finding the derivative with respect to $W$

$$W(1-W)(-w+e+\theta W)$$

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$$\frac d{dW}W(1-W)(-w+e+\theta W)\\=(1-W)(-w+e+\theta W)-W(-w+e+\theta W)+W(1-W)\theta$$ But to simplify this you would probably want to multiply it out, so there doesn't seem much point in doing it in this way.