Find the derivative of x at x = 1. - Vidyadip

Question

Find the derivative of x at x = 1.

✓

Answer

Let $\text{f}(\text{x})=99\text{x}$. Accordingly, $\text{f}'(100)=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f}(100+\text{h})-\text{f}(100)}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{99(100+\text{h})-99(100)}{\text{h}}$$=\lim\limits_{\text{h}\rightarrow0}\frac{99\times100+99\text{h}-99\times100}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{99\text{h}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}(99)=99$ Thus, the derivative of at x = 100 is 99.

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 4 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

Prove the following by using the principle of mathematical induction for all n ∈ N:$\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{(3\text{n}-1)(3\text{n}+2)}=\frac{\text{n}}{(6\text{n}+4)}.$

In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets?

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Differentiate the following from the first principle$\text{f}(\text{x})=\frac{\sin\text{x}}{\text{x}}$

Differentiate the following from the first principle$\text{f}(\text{x})=\frac{\cos\text{x}}{\text{x}}$

Find the equation of the line passing through the point of intersection of the lines 4x - 7y - 3 = 0 and 2x - 3y + 1 = 0 that has equal intercepts on the axes.

Sum the following series to n terms: $\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\ .....\ +\frac{1}{(5\text{n}-4)(5\text{n}+1)}$

Evaluate the following: $\sum\limits^5_\text{r=1}\ ^5\text{C}_{\text{r}}$

Find the mean deviation from the mean for following data:

$x_i$	5	7	9	10	12	15
$f_i$	8	6	2	2	2	6

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?