Final answer:
To find the derivative of the function f(x)=eˣ/3 x⁴, we can apply the product rule.
Step-by-step explanation:
To find the derivative of the function f(x)=eˣ/3 x⁴, we can apply the product rule. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by (u'(x)v(x) + u(x)v'(x)).
In this case, u(x) = eˣ/3 and v(x) = x⁴. We can now calculate the derivatives of u(x) and v(x) separately and then apply the product rule.
Using the chain rule, the derivative of eˣ/3 is (1/3)eˣ/3. The derivative of x⁴ is 4x³. Applying the product rule, the derivative of f(x) is:
f'(x) = (1/3)eˣ/3 * x⁴ + eˣ/3 * 4x³