What is the derivative of 5/sqrtx?

2 Answers
Jan 12, 2017

I got: f'(x)=-5/(2xsqrt(x))

Explanation:

We can use the fact that 1/sqrt(x)=x^(-1/2) and derive as usual as an exponent:
f'(x)=5*-1/2*x^(-1/2-1)=-5/2x^(-3/2)=-5/(2x^(3/2))=-5/(2xsqrt(x))

Jan 12, 2017

(-5)/2 (x^(-3/2))

Explanation:

d/dx 5/sqrtx =d/dx 5 x^(-1/2)

=5 (-1/2)(x^(-3/2))

(-5)/2 (x^(-3/2))