Calculate differentiation of function f(x) e^x+e^ -x e^x-e^ -x w.…

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→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

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

Answer

Need a full question paper?

Explore more

Similar questions