Find the second order derivation of y 3 tan 1x2 y xe 4x

Find the second - order derivation of y = 3 tan - 1(x2) y = xe - 4x y = x2 sin x

Solution

a) dy/dx = 3*2x/(1+x^4) d^2y/dx^2 = 6*(1+x^4) -6x*4x^3 /((1+x^4)^2) b) dy/dx =e^(-4x) -4xe^(-4x) d^2y/dx^2 =-4e^(-4x) -4e^(-4x) +16xe^(-4x) =-8e^(-4x) +16xe^(-4x) c)dy/dx =2xsinx + x^(2) cosx d^2y/dx^2 =2sinx +2xcosx +2xcosx -x^2 sinx =2sinx +4xcosx -x^2 sinx
 Find the second - order derivation of y = 3 tan - 1(x2) y = xe - 4x y = x2 sin xSolution a) dy/dx = 3*2x/(1+x^4) d^2y/dx^2 = 6*(1+x^4) -6x*4x^3 /((1+x^4)^2) b)

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