Determine the forth derivative of this function f(x)=x^4+3x^2-2/√x?

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Answer 1 · 2018-04-10T14:48:19

#y_4=24-105/8x^(-9/2)#

Here,

#f(x)=x^4+3x^2-2/(√x)#

Let,

#y=x^4+3x^2-2(x)^(-1/2)#

Diff. w.r.t. #x#

#y_1=4x^3+6x-2(-1/2)(x^(-1/2-1))#

#=>y_1=4x^3+6x+x^(-3/2)#

Diff. w.r.t. #x#

#y_2=12x^2+6-3/2x^(-5/2)#

Diff. w.r.t. #x#

#=>y_3=24x+0-3/2(-5/2)x^(-7/2)#

#=>y_3=24x+15/4x^(-7/2)#

Diff. w.r.t. #x#

#=>y_4=24+15/4(-7/2)x^(-9/2)#

#=>y_4=24-105/8x^(-9/2)#