Find the derivative of f(x) = 1/x(27,000,000/pi + 6,750,000) + 20pix^2

Question

Can someone help me with this? Thanks.

Answer 1

I am not certain if the 20pi x^2 is in the denominator or not of the first term. If it is really this,
f(x)=[1/(x(27,000,000/pi + 6,750,000)] + 20PI x^2

then work it in two parts, the first, and second term.

f(x)=1/kx + 20 pi x^2
f'= -1/kx^2 + 40PI x
where k= 27E6/PI +6.75E6

Answer 2

Here I'll write it again but distribute the 1/x so you can see it better.

f(x) = (27,000,000/pix)+(6,750,000/x)+20pix^2

Does that help?

Answer 3

The 1/x was only factored out of the first two terms, not out of the
20pi(x^2)

Answer 4

But I get the general idea. I just write 1/x as x^-1 and differentiate that. Makes sense, thanks!