How do you find the derivative of f(x)=5sqrtx?

1 Answer
May 11, 2016

f'(x)=5/(2sqrt(x))

Explanation:

Given,

f(x)=5sqrt(x)

Rewrite the expression using (dy)/(dx) notation.

d/(dx)(5sqrt(x))

Using the multiplication by a constant rule, (c*f)'=c*f', bring out the 5.

=5*d/(dx)(sqrt(x))

Rewrite sqrt(x) using exponents.

=5*d/(dx)(x^(1/2))

Using the power rule, d/(dx)(x^n)=n*x^(n-1), the expression becomes,

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

Simplify.

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

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

=5/2((1)/(sqrt(x)))

=color(green)(|bar(ul(color(white)(a/a)color(black)(5/(2sqrt(x)))color(white)(a/a)|)))