Download App

Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsDerivatives5 Marks
Question
Differentiate the following functions by the product rule and the other method and verify that the answer from both the methods is the same.$(\text{x}+2)(\text{x}+3)$
✓

Answer

Let $\text{u}=(\text{x}+2);\text{v}=(\text{x}+3)$Then, $\text{u}'=1;\text{v}'=1$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[(\text{x}+2)(\text{x}+3)]=(\text{x}+2)1+(\text{x}+3)1$
$=\text{x}+2+\text{x}+3$
$=\text{2x}+5$
Alternate method
$\frac{\text{d}}{\text{dx}}[​(\text{x}+2)(\text{x}+3)]$
$=\frac{\text{d}}{\text{dx}}(\text{x}^2+\text{5x}+6)$
$=\text{2x}+5$

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 "5 Marks Questions" from Derivatives→Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Prove the following by the principle of mathematical induction:
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2^\text{n}}=1-\frac{1}{2^\text{n}}$
→
Show that the equation of the line passing through the origin and making an angle $\theta$ with the line $y = mx + c$ is $\frac{y}{x} = \frac{{m \pm \tan \theta }}{{1 \mp m\tan \theta }}$.
→
Evaluate the following limit:
If $\lim\limits_{\text{x}\rightarrow0}{\text{ kx cosec x}}=\lim\limits_{\text{x}\rightarrow0}\text{ x cosec kx,}{}$ find k.
→
An urn contains $7$ white, $5$ black and $3$ red balls. Two balls are drawn at random. Find the probability that
  1. Both the balls are red.
  2. One ball is red and the other is black.
  3. One ball is white.
→
Find the angle between the lines $\text{y} = (2 - \sqrt{3})(\text{x} + 5)$ and $\text{y} = (2 + \sqrt{3})(\text{x} - 7).$
→
Two ships leave a port at the same time. One goes 24km/ hr in the direction N 38° E and other travels 32km/ hr in the direction S 52° E. Find the distance between the ships at the end of 3hrs.
→
If $\tan\theta+\sin\theta=\text{m}$ and $\tan\theta-\sin\theta=\text{n},$ then prove that $\text{m}^2-\text{n}^2=4\sin\theta\tan\theta$
→
Prove that:
$\frac{\sin\text{A}+\sin\text{B}}{\sin\text{A}-\sin\text{B}}=\tan\Big(\frac{\text{A}-\text{B}}{2}\Big)\cot\Big(\frac{\text{A}-\text{B}}{2}\Big)$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{3\sin^2\text{x}-2\sin\text{x}^2}{3\text{x}^2}$
→
Find the term independent of x in the expansion of the following expressions:
$\Big(2\text{x}+\frac{1}{3\text{x}^{2}}\Big)^{9}$
→