Question

Differentiate the function v = x^(1/3) * x²?

Answer 1

To differentiate the function v = x^(1/3) * x², use the product rule of differentiation.

Step-by-step explanation:

To differentiate the function v = x^(1/3) * x², we can use the product rule of differentiation. The product rule states that if we have two functions, u(x) and v(x), their derivative is given by (u(x) * v'(x)) + (u'(x) * v(x)).

Applying the product rule to the given function, we have:

v'(x) = (x^(1/3) * 2x) + (1/3 * x^(1/3) * x²)

Simplifying this, we get:

v'(x) = 2x^(4/3) + (1/3) * x^(7/3)