If xe^ xy =y+e^ 2x , then at x=0, , dy dx is equal to - - Vidyadip

MCQ

If $xe^{xy}=y+e^{\sin 2x} ,$ then at $x=0, \, \frac{dy}{dx}$ is equal to -

✓
$-1$
B
$1$
C
$0$
D
$2$

✓

Answer

Correct option: A.

$-1$

a
$e^{x y} \cdot 1+x e^{x y}\left(y+x \frac{d y}{d x}\right)=\frac{d y}{d x}+e^{\sin 2 x} \cdot \cos 2 x$

at $x=0$

$1+0=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{x}=0}+2 \Rightarrow\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{x}=0}=-1$

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 STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The corner points of the feasible region determined by the system of linear constraints are (0, 10),(5, 5),(15, 15),(0, 20). Let z = px + qy where p, q > 0. Condition on p and q so that the maximum of z occurs at both the points (15, 15) and (0, 20) is __________:

Let $\phi(\text{x})=\text{f}(\text{x})+\text{f}(2\text{a}-\text{x})$ and f'(x) > 0 for all $\text{x}\in[0,\text{a}].$ Then, $\phi(\text{x}):$

Choose the correct answer from the given four option.
The degree of the differential equation $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+\Big(\frac{\text{d}\text{y}}{\text{d}\text{x}}\Big)^3+6\text{y}^5=0$ is:

For any two events $A$ and $B,$ if $P(\bar{A})=\frac{1}{2}, P(\bar{B})=\frac{2}{3}$ and $P(A \cap B)=\frac{1}{4}$, then $P(\bar{A} / \bar{B})$ equals:

Let, $f(x)=\left\{\begin{array}{l} x \sin \left(\frac{1}{x}\right) \text { when } x \neq 0 \\ 1 \text { when } x=0 \end{array}\right\}$ and $A=\{x \in R: f(x)=1\} .$ Then, $A$ has

If $A$ is $3×4$ matrix and $ B$ is a matrix such that $A'B$ and $BA'$ are both defined. Then $B $ is of the type

The system of equations ${x_1} - {x_2} + {x_3} = 2,$ $\,3{x_1} - {x_2} + 2{x_3} = - 6$ and $3{x_1} + {x_2} + {x_3} = - 18$ has

The additive inverse of $A+B$, where $A$ and $B$ are given as $A=\left[\begin{array}{ll}2 & 5 \\ 9 & 3\end{array}\right], B=\left[\begin{array}{cc}-1 & 2 \\ 3 & -9\end{array}\right]$ is

The differential coefficient of ${\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}$ $w.r.t.$ ${\sin ^{ - 1}}{{2x} \over {1 + {x^2}}}$ is

Objective function of an LPP is