How do you differentiate # (xsinx)/(x^2+1)#?

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Answer 1 · 2016-12-12T20:33:35

We'll be using the product rule with the quotient rule:

Let's think of your function as:

#(f(x)*g(x))/(h(x))#

Where:
#f(x)=x#
#g(x)=sin(x)#
#h(x)=x^2+1#

Thus, the derivative is:

#[d/dx(f(x)*g(x))*h(x)-(f(x)*g(x))*d/dx(h(x))]/(h(x)^2)#

Plug in our functions and find the derivatives:

#[d/dx(xsinx)*(x^2+1)-(xsinx)*d/dx(x^2+1)]/((x^2+1)^2)#

#=[(sinx+xcosx)(x^2+1)-(2x^2sinx)]/(x^2+1)^2#