Find the derivative of the following functions from first princip… - Vidyadip

Question

Find the derivative of the following functions from first principle: $-\text{x}$

✓

Answer

Let f(x) = –x. Accordingly, f(x + h) = -(x + h) By first principle, $\text{f}'(\text{x})=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(x+h)}-\text{f(x)}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{-(\text{x+h})-(-\text{x})}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{-\text{x}-\text{h}+\text{x}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{-\text{h}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}(-1)=-1$

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 2 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

In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together?

A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is: A black king.

Show the following quadratic equation by factorization method: $x^2+(1-2 i) x-2 i=0$

Find: The $12^{th}$ term of the G.P. $\frac{1}{\text{a}^3\text{x}^3},\text{ax},\text{a}^5\text{x}^5\dots$

How many 4-letter codes can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Find the coordinates of the centre and radius of each of the following circles: $2\text{x}^2+2\text{y}^2-3\text{x}+5\text{y}=7$

Evaluate the following one sided limits: $\lim\limits_{\text{x}\rightarrow-8^+}\frac{2\text{x}}{\text{x}+8}.$

In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

Differentiate the following functions with respect to x:$\frac{\text{e}^\text{x}-\tan\text{x}}{\cot\text{x}-\text{x}^\text{n}}$

Find the distance between the parallel lines 3x – 4y + 7 = 0 and 3x – 4y + 5 = 0