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

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Answer 1 · 2016-05-05T17:39:08

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

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)|)))#