Final answer:
To differentiate y = x e^-x^4, we can use the product rule of differentiation. The product rule states that if we have the product of two functions, then the derivative of the product is given by (f(x) * g'(x)) + (f'(x) * g(x)). In this case, the derivative of y is -4x^4 * e^-x^4 + e^-x^4.
Step-by-step explanation:
To differentiate y = x e-x4, we can use the product rule of differentiation. The product rule states that if we have the product of two functions, say f(x) and g(x), then the derivative of the product is given by (f(x) * g'(x)) + (f'(x) * g(x)). In this case, f(x) = x and g(x) = e-x4. We need to find f'(x) and g'(x) first. The derivative of f(x) = x is f'(x) = 1 and the derivative of g(x) = e-x4 is g'(x) = -4x3 * e-x4. Substituting these values into the product rule formula, we get the derivative of y as y' = (x * -4x3 * e-x4) + (1 * e-x4). Simplifying further, we have y' = -4x4 * e-x4 + e-x4.