Download App

PART - 2 CH - 12 Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPART - 2 CH - 12 Limits and Derivatives3 Marks
Question
Calculate differentiation of function $f(x)$ $\frac{e^x+e^{-x}}{e^x-e^{-x}}$ $\text{w.r.t.x.}$
✓

Answer

Let $y=\frac{e^x+e^{-x}}{e^x-e^{-x}}$
On differentiating both sides $\text {w.r.t.x}:$
$\frac{d y}{d x}=\frac{\left(e^x-e^{-x}\right) \frac{d}{d x}\left(e^x+e^{-x}\right)-\left(e^x+e^{-x}\right) \frac{d}{d x}\left(e^x-e^{-x}\right)}{\left(e^x-e^{-x}\right)^2}$
$=\frac{\left(e^x-e^{-x}\right)\left(e^x-e^{-x}\right)-\left(e^x+e^{-x}\right)\left(e^x+e^{-x}\right)}{\left(e^x-e^{-x}\right)^2}$
$=\frac{\left(e^x-e^{-x}\right)^2-\left(e^x+e^{-x}\right)^2}{\left(e^x-e^{-x}\right)^2}$
$=\frac{\left(e^x-e^{-x}+e^x+e^{-x}\right)\left(e^x-e^{-x}-e^x-e^{-x}\right)}{\left(e^x-e^{-x}\right)^2}$
$=\frac{2 e^x \times\left(-2 e^{-x}\right)}{\left(e^x-e^{-x}\right)^2}=\frac{-4 e^0}{\left(e^x-e^{-x}\right)^2}=\frac{-4 \times 1}{\left(e^x-e^{-x}\right)^2}$
$=\frac{-4}{\left(e^x-e^{-x}\right)^2}$

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 "3 Marks Question" from PART - 2 CH - 12 Limits and Derivatives→PART - 2 CH - 12 Limits and 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 that:
$\cos4\text{x}=1-8\cos^2\text{x}+8\cos^4\text{x}$
→
Find the middle terms(s) in the expansion of:
$(1+3\text{x}+3\text{x}^{2}+\text{x}^{3})^{2\text{n}}$
→
Show that the middle term in the expansion of $\Big(\text{x}-\frac{1}{\text{x}}\Big)^{2\text{n}}$ is $\frac{1\times3\times5\times....(2\text{n}-1)}{\text{n}!}\times(-2)^\text{n}.$
→
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
→
Prove that:
$\big(\cos\alpha+\cos\beta^2\big)+\big(\sin\alpha+\sin\beta\big)^2=2\cos^2\Big(\frac{\alpha-\beta}{2}\Big)$
→
Evaluate the following limit:
$\lim\limits_{\text{n}\rightarrow\infty}\frac{1^2+2^2+\ \dots+\text{n}^2}{\text{n}^4}$
→
If ${^\text{2n}}\text{C}_{\text{3}}:{^\text{n}}\text{C}_{\text{2}}=44:3,$ find n.
→
How many terms of G.P. $3, 3^2 , 3^3 ......$ are needed to give the sum $120?$
→
Find the lengths of the medians of the triangle with vertices $A (0, 0, 6), B (0, 4, 0)$ and $C (6, 0, 0).$
→
Solve the following system of equations in R.
|4 - x| + 1 < 3
→