What is the derivative of -4/x^2?

1 Answer
May 5, 2016

d/(dx)(-4/x^2)=8x^(-3)

Explanation:

Given,

-4/x^2

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

d/(dx)(-4/x^2)

Break down the fraction.

=d/(dx)(-4*1/x^2)

Using the multiplication by a constant rule, (c*f)'=c*f', bring out the -4.

=-4*d/(dx)(1/x^2)

Rewrite 1/x^2 using exponents.

=-4*d/(dx)(x^-2)

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

=-4*-2x^(-2-1)

Simplify.

=color(green)(|bar(ul(color(white)(a/a)color(black)(8x^-3)color(white)(a/a)|)))