найти производную функции f(x)=(2x^5+x^4-3x^2+5x+6)/3x^2 f(x)=-x^5/5+2x^3/3-x^2+x+5/x^2...

Question

найти производную функции

f(x)=(2x^5+x^4-3x^2+5x+6)/3x^2

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

f(x)=2x^7/7-3x^5/10+4x^3-x-10

g(t)=-1/t^4+1/t^2-1/4t

Answer 1

f'(x)=((2x^5+x^4-3x^2+5x+6)/3x^2)'=(2/3x³+1/3*x²-1+5/(3x)+2/x²)'=3*2/3*x²+2/3*x-5/(x²)-4*x⁻³=2x²+2/3x-5/x²-4/x³
f'(x)=-(x^5/5+2x^3/3-x^2+x+5/x^2)'=-5/5*x⁴-2*3x²+2x-1+10/x³=-x⁴-6x²+2x-1+10/x³f'(x)=(2x^7/7-3x^5/10+4x^3-x-10)'=2*7/7*x⁶-3*5/10*x⁴+4*3*x²-1=2x⁶-1.5x⁴+12x²-1
g'(t)=(-1/t^4+1/t^2-1/4t)'=-1*(-4)*t⁻⁵-2*t⁻³-1/4=4/t⁵-2/t²-1/4