Verified answer

f(x) = 1/(sqrt(x^2+1).........equation(1)

f'(x) = -x/((x^2)+1)^(3/2).....equation(2)

We know that the linearization:

L(x)=f(a)+f'(a)(x-a) ......equation(3) where a = 1 here given

f(1)= 1/(2)^(1/2).........by plugging in x=1 into equation(1)

f'(1) = -1/2^(3/2).........by plugging in x=1 into equation(2)

Now plugin f(1), f'(1) and a = 1 into equation (3) and we get:

L(x) = 3/(2^(3/2)) - x/(2^(3/2))

So we can write: y = 3/(2^(3/2)) - x/(2^(3/2))......[Answer]

sin(a million/x)-x*cos(a million/x)(a million/x^2) i think of this is real employing the product rule then the chain rule on the final section. "spinoff of x circumstances sin(a million/x) plus x circumstances the spinoff of sin(a million/x)"