How do you find the derivative of x*x^(1/2)?

1 Answer
Aug 8, 2015

d/(dx) (x*x^(1/2)) = d/(dx) x^(3/2) = 3/2x^(1/2)

or

d/(dx) (x*x^(1/2)) = (d/(dx) x) * x^(1/2) + x * (d/(dx)x^(1/2))

=1*x^(1/2)+x*(1/2)x^(-1/2) = x^(1/2)+1/2 x^(1/2) = 3/2 x^(1/2)

Explanation:

We can either multiply x*x^(1/2) = x^(3/2) first then use the power rule, or we can use the product rule, using the power rule on each part.

Power Rule
d/(dx) x^k = k*x^(k-1)

Product Rule
d/(dx) (f(x)*g(x)) = f'(x)g(x)+f(x)g'(x)