How do you find the derivative of x*x^(1/2)xx12?

1 Answer
Aug 8, 2015

d/(dx) (x*x^(1/2)) = d/(dx) x^(3/2) = 3/2x^(1/2)ddx(xx12)=ddxx32=32x12

or

d/(dx) (x*x^(1/2)) = (d/(dx) x) * x^(1/2) + x * (d/(dx)x^(1/2))ddx(xx12)=(ddxx)x12+x(ddxx12)

=1*x^(1/2)+x*(1/2)x^(-1/2) = x^(1/2)+1/2 x^(1/2) = 3/2 x^(1/2)=1x12+x(12)x12=x12+12x12=32x12

Explanation:

We can either multiply x*x^(1/2) = x^(3/2)xx12=x32 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)ddxxk=kxk1

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