If y= ( e^x ), then d y d x is - Vidyadip

Question

If $y=\log \left(\sin e^x\right)$, then $\frac{d y}{d x}$ is

✓

Answer

$y=\log \left(\sin e^x\right)$
Differentiating w.r.t. $x$, we get
$\begin{aligned}
\frac{d y}{d x}= & \frac{1}{\sin e^x} \cdot \frac{d}{d x}\left(\sin e^x\right)=\frac{1}{\sin e^x} \cos e^x \cdot \frac{d}{d x} e^x=\frac{1}{\sin e^x} \cos e^x \cdot e^x \\
& =e^x \cot e^x
\end{aligned}
$

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 "M.C.Q (1 Marks)" from Continuity and Differentiability→Continuity and Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{f(x)}=|\log_\text{e}|\text{x}||,$ then:

f(x) is continuous and differentiable for all x in its domain.
f(x) is continuous for all for all × in its domain but not differentiable at $\text{x}=\pm1$
f(x) is neither continuous nor differentiable at $\text{x}=\pm1$
None of these.

$\int\log_{10}\text{xdx}=$

$\log_\text{e}10.\text{x}\log_\text{e}(\frac{\text{x}}{\text{e}})+\text{c}$
$\log_{10}\text{e}.\text{x}\log_\text{e}(\frac{\text{x}}{\text{e}})+\text{c}$
$(\text{x}-1)\log_\text{e}\text{x}+\text{c}$
$\frac{1}{\text{x}}+\text{c}$

If $\cos\alpha,\cos\beta,\cos\gamma$ are the direction cosines of a vector $\vec{\text{a}}$ then $\cos2\alpha+\cos2\beta+\cos2\gamma$ is equal to:

If R is a relation on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3)}, then R is:

Reflexive.
Symmetric.
Transitive.
All the three options.

If a matrix $A$ is both symmetric and skew$-$symmetric, then:

A set is said to be convex if

The area bounded by the curve $y = x|x|$ and the ordinates $x = -1$ and $x = 1$ is given by:

If $\text{x}=2\text{ at},\text{y}=\text{at}^2,$ where a is a constant, then $\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ at}\ \text{x}=\frac{1}{2}$ is:

$\frac{1}{2}\text{a}$
1
2a
None of these

$\text{f}(\text{x})=2\text{x}-\tan^{-1}-\log\Big\{\text{x}+\sqrt{\text{x}^2+1}\Big\}$ is monotonically increasing when:

$\text{x}>0$
$\text{x}<0$
$\text{x}\in\text{R}$
$\text{x}\in\text{R}-\{0\}$

If $\frac{\text{dy}}{\text{dx}}=\cos(2\text{x})$ then y =

$\frac{\sin(2\text{x)}}{\text{2}}+\text{c}$
$2\sin(2\text{x})+\text{c}$
$\frac{\sin(\text{x})}{2}+\text{c}$
None of these