Find the derivative of function (-x)-1 from first principle. - Vidyadip

Question

Find the derivative of function (-x)^-1from first principle.

✓

Answer

Here f(x) = (-x)^-1 = $- \frac{1}{x}$
Then f(x + h) = $- \frac{1}{{x + h}}$
We know that $f{\text{'}}(x) = \mathop {\lim }\limits_{h \to 0} \frac{{f(x + h) - f(x)}}{h}$
$\Rightarrow \;f{\text{'}}(x) = \mathop {\lim }\limits_{h \to 0} \frac{{ - \frac{1}{{x + h}} - \left( { - \frac{1}{x}} \right)}}{h}$$ = \mathop {\lim }\limits_{h \to 0} \frac{{ - x + x + h}}{{hx(x + h)}}$
$= \mathop {\lim }\limits_{h \to 0} \frac{h}{{hx(x + h)}} = \frac{1}{{{x^2}}}$

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 "1 Marks Question" from Limits and Derivatives→Limits and Derivatives — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write the area of the circle passing through (-2, 6) and having its centre at (1, 2).

If $\pi<\theta<2\pi$ and $\text{z}=1+\cos\theta+\text{i}\sin\theta,$ then write the value of $|\text{z}|.$

The set of all positive integers whose cube is odd.

List all events associated with the random experiment of tossing of two coins. How many of them are elementary events.

Evaluate the following:
$\cos80^\circ\cos20^\circ+\sin80^\circ\sin20^\circ$

Equation $x^2+y^2+2 g x+2 f y+c=0$ always represents a circle and write its centre and radius.

If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11}, and D = {10, 11, 12, 13, 14}. Find:
$\text{B}\cup\text{C}$

If n arithmetic means are inserted between 1 and 31 such that the ratio of the first mean and n^th mean is 3 : 29, then the value of n is:

10
12
13
14

Write down the negation of following compound statement:
x = 2 and x = 3 are roots of the Quadratic equation x² - 5x + 6 = 0.

If A and B are two sets such that n(A) = 115, n(B) = 326 and n(A - B) = 47, then write $\text{n(A}\cup\text{B)}.$