How do you calculate the derivative of #(4x- 3)/(sqrt(2x^2 +1))#?

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Answer 1 · 2015-04-02T01:09:41

You can use the product rule to find the derivative.

Rewrite the function as follows

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

Using the product rule

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

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

#dy/dx=(2x^2+1)^(-3/2)[4(2x^2+1)-2x(4x-3)]#

#dy/dx=(2x^2+1)^(-3/2)[8x^2+4-8x^2+6x] #

#dy/dx=(2x^2+1)^(-3/2)[4+6x] #

#dy/dx=2(2x^2+1)^(-3/2)[2+3x] #

#dy/dx=(2(2+3x))/(2x^2+1)^(3/2) #