# Finding the tangent's gradient at 1!

#### Katjalc

Hello,

I am currently learning about calculus.
I have an assignment where I have to find out which point on the curve f(x)=x/x^2+1 the tangent have gradient at 1. I am not sure on how to calculate this, so if anybody can help me, it would be much appreciated

#### skeeter

MHF Helper
Hello,

I am currently learning about calculus.
I have an assignment where I have to find out which point on the curve f(x)=x/(x^2+1) the tangent have gradient at 1. I am not sure on how to calculate this, so if anybody can help me, it would be much appreciated
are you trying to find the gradient at $x = 1$, or where the tangent to the curve has gradient = $1$ ?

in either case, use the quotient rule to find $f'(x)$ ...

$f'(x) = \dfrac{(x^2+1)(1)-(x)(2x)}{(x^2+1)^2}$

if you're trying to find the gradient at $x=1$, then evaluate $f'(1)$

if you're trying to find where the gradient equals $1$, then solve $f'(x)=1$ for $x$.

oh, and use grouping symbols to make your expression clear

Last edited:

#### Katjalc

But what do you mean by using "grouping symbols"? Like brackets or?

#### skeeter

MHF Helper
But what do you mean by using "grouping symbols"? Like brackets or?
you posted
... point on the curve f(x)=x/x^2+1 ...
that expression could be interpreted as $\dfrac{x}{x^2} + 1$ in the absence of grouping symbols.

Grouping symbols that are used most often are (parentheses) and/or [brackets], like so ...

f(x) = x/(x^2+1)