Пошаговое объяснение:
1. y'=2x(2x^3+x^(1/2))+(x^2+1)(6x^2+1/2*1/√x))=
=4x^4+2x√x+6x^4+(1/2)x√x+6x^2+1/2√x=
=10x^4+(5/2)x√x+1/2√x
2. y'=2[(3x^2-1)(1+2x^5)-(x^3-x)*10x^4)]/(1+2x^5)^2=
=2*[3x^2-1-2x^5+6x^7-10x^7+10x^5]/(1+2x^5)^2=
2*[-4x^7+8x^5+3x^2-1]/(1+2x^5)^2
3. y'=7^xln7cos2x-2*7^xsin2x=7^x(ln7*cos2x-2sin2x)
Пошаговое объяснение:
1. y'=2x(2x^3+x^(1/2))+(x^2+1)(6x^2+1/2*1/√x))=
=4x^4+2x√x+6x^4+(1/2)x√x+6x^2+1/2√x=
=10x^4+(5/2)x√x+1/2√x
2. y'=2[(3x^2-1)(1+2x^5)-(x^3-x)*10x^4)]/(1+2x^5)^2=
=2*[3x^2-1-2x^5+6x^7-10x^7+10x^5]/(1+2x^5)^2=
2*[-4x^7+8x^5+3x^2-1]/(1+2x^5)^2
3. y'=7^xln7cos2x-2*7^xsin2x=7^x(ln7*cos2x-2sin2x)