Find the derivative of f(x) = x+1 x - Vidyadip

Question

Find the derivative of f(x) = $\frac{x+1}{x}$

✓

Answer

The given function is defined everywhere except at x = 0. We use the quotient rule with u = x + 1 and v = x. Hence u′ = 1 and v′ = 1.
Therefore, we have,
$\frac{d f(x)}{d x}=\frac{d}{d x}\left(\frac{x+1}{x}\right)=\frac{d}{d x}\left(\frac{u}{v}\right)$ $=\frac{u^{\prime} v-u v^{\prime}}{v^{2}}=\frac{1(x)-(x+1) 1}{x^{2}}=-\frac{1}{x^{2}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 1 marks)" from LIMITS AND DERIVATIVES→LIMITS AND DERIVATIVES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let A = {1, 2, 3} and $\text{R}=\{(\text{a, b}):|\text{a}^2-\text{b}^2|\leq5,\text{a, b}\in\text{A}\}.$ Then write R as set of ordered pairs.

Evaluate the following limits in Exercise: $\lim\limits_{\text{x} \rightarrow4}\frac{4\text{x}+3}{\text{x}-2}$

State whether the two lines in the following are parallel, perpendicular or neither. Through (9, 5) and (-1, 1); through (3, -5) and (8, -3)

Write the distance between the lines 4x + 3y - 11 = 0 and 8x + 6y - 15 = 0.

Let f and g be two real functions given by: f = {(0, 1), (2, 0), (3, -4), (4, 2), (5, 1)} and g = {(1, 0), (2, 2), (3, -1), (4, 4), (5, 3)} Find the domain of fg.

If A = {1, 2, 3}, B = {4, 5, 6}, the given following are relations from A to B? Give reason in support of your answer.
{(1, 6), (3,4), (5, 2)}

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow-1}\frac{\text{x}^3-3\text{x}+1}{\text{x}-1}$

The given collections are sets or not? Justify your answer:
A collection of novels written by Munshi, Prem, Chand.

A coin is tossed 3 times and the out comes are recorded. How many possible outcomes are there?

Find the derivative of the function 5sec x + 4cos x