Question

If f(x) = (x + 1)/x then df(x)/dx is
(a) 1/x
(b)-1/x
(C)-1/2
(d) 1/2
a
ь
C
d​

Answer 1

-1/x is the answer of your question.

Answer 2

If  $f(x) = \frac{x+1}{x}$ then df(x)/ dx is -1/x²

The equation given is,

$f(x) = \frac{x+1}{x}$

Process 1:

Now, we can simplify the equation like the following,

$f(x)=1+\frac{1}{x}$

Next, differentiate this equation using simple derivative formula, i.e. ,

$\frac{d}{dx} (x^n)$ = $nx^n$⁻¹

Given,

$f(x)=1+\frac{1}{x}$

By differentiating this equation, we get,

$\frac{d}{dx} {f(x)}$ = $\frac{d}{dx} (1) + \frac{d}{dx} (x$⁻¹$)$

⇒ $\frac{d}{dx} {f(x)}$  = 0 + [ -1 × $x$⁽⁻¹⁻¹⁾]  [∵ derivative of any constant is 0]

⇒ $\frac{d}{dx} {f(x)}$ =  $\frac{-1}{x^{2} }$

∴ The answer is -1/x².

Process 2:

We can also use the formula of differentiating of an equation given as division.

In that case we should use the formula,

$\frac{d}{dx} {\frac{f(x)}{g(x)} = \frac{g(x)\frac{d}{dx} f(x) - f(x) \frac{d}{dx}g(x) }{g(x^2)}$

By replacing f(x) with (x+1) and g(x) with x, and solving the equation, we also get the answer as -1/x².

∴ In both the cases, we get the same answer, i.e., -1/x².