f(x)=-4x^5+3x^2-5/x^2f(x)=−4x5+3x2−5x2
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)=0⋅x2−2x⋅5(x2)2=−10xx4
d/(d x) f(x)=-20x^4+6x-(10x)/x^4ddxf(x)=−20x4+6x−10xx4
d/(d x) f(x)=(-20x^(16)+6x^5-10x)/x^4ddxf(x)=−20x16+6x5−10xx4