Question
Find derivative of $f ( x )=x^{10}$ using definition.
✓
Answer
Here, $f(x) = x^{10}$
$\therefore f(x + h) = (x + h)^{10}$
Take, $x + h = t.$ When $h \rightarrow 0, t \rightarrow x$ and $h = t – x$
Hence, $f(x) = x^{10}$ then $f ‘(x) = 10x^9$
$\therefore f(x + h) = (x + h)^{10}$
Take, $x + h = t.$ When $h \rightarrow 0, t \rightarrow x$ and $h = t – x$
Hence, $f(x) = x^{10}$ then $f ‘(x) = 10x^9$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
$\lim _{x \rightarrow 2} \frac{x^2-5 x+6}{x^2-6 x+8} $
→State properties of binomial distribution.
If $P(A)=\frac{1}{3}, P(B)=\frac{2}{3}$ and $P(A / B)=\frac{1}{4}$, find $P\left(A^{\prime} \cap B^{\prime}\right)$.
→The prices per unit $R$ of six food items in the year $2014$ and $2015$ are given in the following table. Taking $2014$ as the base year, compute the general index number for the price of food items and state the overall rise in prices of these food items.
→Fit a linear equation from the following data about the variable $y$ of a time series.
$n=6, \Sigma y=378, \Sigma t y=1399$
→$n=6, \Sigma y=378, \Sigma t y=1399$
A problem in Mathematics is given to Dhyan, Kaushal and Namrata to solve. The probabilities of them solving the problem correctly are $\frac{2}{3}, \frac{3}{4}$, and $\frac{1}{2}$ respectively. Find the probability that the problem is solved correctly.OR $4$ couples $($husband-wife$)$ attend a party. Two persons are randomly selected from these $8$ persons. Find the probability that the selected two persons are, $(1)$ husband and wife, $(2)$ One man and one woman who are not husband and wife. Find the probability.
→Obtain the chain base index number from the fixed base index nuimbers given below with the year $2007-08$ a the base year for the wholesale prices of machines and equipments :
→| year | $2008-09$ | $2009-10$ | $2010-11$ | $2011-12$ | $2012-13$ |
| Index number of machines and equipments | $117.4$ | $118$ | $121.3$ | $125.1$ | $128.4$ |
Find $\frac{d y}{d x}$ if $y =\frac{a x+b}{b x+a}$ (a and $b$ are constants).
→$(5 x-1) \cdot(y+1)=9$
→A normal variable $X$ has the following probability density function :
$f(x) = \frac{1}{6 \sqrt{2 \pi}} e^{-\frac{1}{72}(x-100)^{2}}, – \infty < x < \infty $
For this distribution, obtain the estimated limits for the exact middle $50 \%$ of the observations.
→$f(x) = \frac{1}{6 \sqrt{2 \pi}} e^{-\frac{1}{72}(x-100)^{2}}, – \infty < x < \infty $
For this distribution, obtain the estimated limits for the exact middle $50 \%$ of the observations.