Question

differentiate with respect to X (x+1)^2/
(x+2)^3 (x+3)^4​

Answer 1

Answer:

N/A

Step-by-step explanation:

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Solution:   Let y=(x+1)2(x+2)3(x+3)4

∴logy=log{(x+1)2.(x+2)3(x+3)4}

=log(x+1)2+log(x+2)3+log(x+3)4

and ddylogy.dydx=dydx=ddx[2log(x+1)]+ddx[3log(x+2)]+ddx[4log(logx)=1x]

1y.dydx=2(x+1).ddx(x+1)+3.1(x+2).ddx(x+2)+4.1(x+3).ddx(x+3)[∵ddx(logx)=1x]

=[2x+1+3x+2+4x+3]

∴dydx=y[2(x+1)+3(x+2)+4(x+3)]

=(x+1)2.(x+2)3.(x+3)4[2(x+1)+3(x+2)+4(x+3)]

=(x+1)2.(x+2)3.(x+3)4

[2(x+2)(x+3)+3(x+1)(x+3)+4(x+1)(x+2)(x+1)(x+2)(x+3)]

=(x+1)2(x+2)3(x+3)4(x+1)(x+2)(x+3)

[2(x2+5x+6)+3(x2+4x+3)+4(x2+3x+2)]

=(x+1)(x+2)2(x+3)3

[2x2+10x+12+13x2+12+9+4x2+12x+8]

=(x+1)(x+2)2(x+3)3[9x2+34x+29]