Question

A)y=sgrt x^4-3x^2+7x
B)y=(x^5+2x^3)^25
C)y=ctg(pi/4-3x)/(4-5x)^2
найти производную помогите

Answer 1

A) y'=1/2 * (x^4-3x^2+7x)^(-1/2) * (x^4-3x^2+7x)' = 1/2 * 1/sqrt(x^4-3x^2+7x) * (4x^3 - 6x+7)

B) y'=25*(x^5+2x^3)^24 * (5x^4+6x)

C) y'=-((pi/4-3x)/(4-5x)^2)'/sin²((pi/4-3x)/(4-5x)^2)=

=(-3(4-5x)^2+10(pi/4-3x)(4-5x))/(4-5x)^4*sin²((pi/4-3x)/(4-5x)^2)

***((pi/4-3x)/(4-5x)^2)'=((pi/4-3x)'(4-5x)^2 - (pi/4-3x)((4-5x)^2)')/(4-5x)^4=

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