How do you find the derivative of f(x)=-4x^5+3x^2-5/x^2f(x)=4x5+3x25x2?

1 Answer
Apr 9, 2017

d/(d x) f(x)=(-20x^(16)+6x^5-10x)/x^4ddxf(x)=20x16+6x510xx4

Explanation:

f(x)=-4x^5+3x^2-5/x^2f(x)=4x5+3x25x2

d/(d x) f(x)=color(red)(d/(d x)( -4x^5))+color(blue)( d/(d x)(3x^2))-color(green)(d/(d x)(5/x^2))ddxf(x)=ddx(4x5)+ddx(3x2)ddx(5x2)

color(red)(d/(d x)( -4x^5))=-20x^4ddx(4x5)=20x4

color(blue)(d/(d x)(3x^2))=6xddx(3x2)=6x

color(green)(d/(d x)(5/x^2))=(0*x^2-2x*5)/(x^2)^2=(-10x)/x^4ddx(5x2)=0x22x5(x2)2=10xx4

d/(d x) f(x)=-20x^4+6x-(10x)/x^4ddxf(x)=20x4+6x10xx4

d/(d x) f(x)=(-20x^(16)+6x^5-10x)/x^4ddxf(x)=20x16+6x510xx4