Question
Differentiate the $\frac{{{e^x}}}{{\sin x}}$ w.r.t x.
✓
Answer
Let $y = \frac{{{e^x}}}{{\sin x}}$
$\therefore \frac{{dy}}{{dx}} = \frac{{\sin x\frac{d}{{dx}}{e^x} - {e^x}\frac{d}{{dx}}\sin x}}{{{{\sin }^2}x}}$ [By quotient rule]
$= \frac{{\sin x.{e^x} - {e^x}\cos x}}{{{{\sin }^2}x}}$
$= {e^x}\frac{{\left( {\sin x - \cos x} \right)}}{{{{\sin }^2}x}}$
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
Evaluate:
$\int\Big(\frac{2\cos^2\text{x}-\cos2\text{x}}{\cos^2\text{x}}\Big)\text{dx}$
→$\int\Big(\frac{2\cos^2\text{x}-\cos2\text{x}}{\cos^2\text{x}}\Big)\text{dx}$
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.
none.
none.
Write a value of $\int\text{e}^{\text{ax}}\{\text{a }\text{f(x)}+\text{f}'(\text{x})\}\text{ dx}$
→If $\text{A}=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix},\text{ B}=\text{diag}\begin{pmatrix}1&1&-4\end{pmatrix}$ and $\text{C}=\text{diag}\begin{pmatrix}-6&3&4\end{pmatrix},$ find.
A - 2B
→A - 2B
Find the principal values of the following:
$\tan^{-1}\Big(2\cos\frac{2\pi}{3}\Big)$
→$\tan^{-1}\Big(2\cos\frac{2\pi}{3}\Big)$
If f(x) = x + 1 then write the value of $\frac{\text{d}}{\text{dx}}\text{ fof }\text{(x)}.$
→A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x, y): y is one half of x; x, y ∈ A} is a relation on A, then write R as a set of ordered pairs.
If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.
If $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix},$ write the value of x.
→Which of the following graphs represents a one-one function?
