Download App

Derivatives — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives4 Marks
Question
Differentiate the following from first principle$\tan\text{2x}$
✓

Answer

$\text{f}(\text{x})=\tan\text{2x}$$\text{f}'(\text{x})=\lim_\limits{\text{h}\rightarrow0}\frac{\text{f}(\text{x}+\text{h})-\text{f}(\text{x})}{\text{h}}$
$=\lim_\limits{\text{h}\rightarrow0}\frac{\tan2(\text{x}+\text{h})-\tan2\text{x}}{\text{h}}$
$=\lim_\limits{\text{h}\rightarrow0}\frac{\sin(\text{2x}+\text{2h}-\text{2x})}{\text{h}.\cos(\text{2x}+\text{2h})\cos\text{2x}}\ \Big[\because\tan\text{A}-\tan\text{B}=\frac{\sin\text{A}-\text{B}}{\cos\text{A}.\cos{\text{B}}}\Big]$
$=\lim_\limits{\text{h}\rightarrow0}\frac{\sin2\text{h}}{\text{h}.\cos(\text{2x}+\text{2h})\cos2\text{x}}$
$=\lim_\limits{\text{h}\rightarrow0}\Big(\frac{\sin2\text{h}}{2\text{h}}\Big)\times\frac{1\times2}{\cos(\text{2h}+\text{2x})\cos2\text{x}}$
$=\frac{2}{\cos2\text{x}.\cos2\text{x}}\ \Big[\because\lim_\limits{\text{h}\rightarrow0}\frac{\sin2\text{h}}{2\text{h}}=1\Big]$
$=2\sec^22\text{x}\ \Big[\because\frac{1}{\cos^2\text{x}}=\sec^2\text{x}\Big]$

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 Derivatives→Derivatives — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the eccentricity, coordinates of foci, length of the latus-rectum of the following ellipse:$25\text{x}^2+16\text{y}^2=1600.$
→
Solve the system of inequality graphically: x + 2y $\le$ 10, x + y $\ge$ 1, x – y $\le$ 0, x $\ge$ 0, y $\ge$ 0
→
In an examination, a student has to answer 4 questions out of 5 questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
→
A rod of length 12cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with x-axis.
→
Prove that: $4\cos\text{x}\cos\Big(\frac{\pi}{3}+\text{x}\Big)\cos\Big({\frac{\pi}{3}-\text{x}}\Big)=\cos3\text{x}$
→
If a, b, c, are in G.P., prove that: $(\text{a}^2+\text{b}^2),(\text{b}^2+\text{c}^2),(\text{c}^2+\text{d}^2)\text{ are in G.P.}$
→
Find the angle between the lines x = a and by + c = 0.
→
Find the equation of the hyperbola whose, Focus is (2, 1) directrix is $2\text{x}+3\text{y}=1$ and eccentricity = 2
→
Find the general solution for each of the following equations: $\cos3\text{x}+\cos\text{x}-\cos2\text{x}=0$
→
Solve the following equations: $4\sin\text{x}\cos\text{x}+2\sin\text{x}+2\cos\text{x}+1=0$
→