If x e^{xy} = y + sin^2 x, then the value of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given equation: $x e^{xy} = y + \sin^2 x$. Step $1$: Find the value of $y$ at $x = 0$. Substitute $x = 0$ into the equation: $0 \cdot e^{0} = y +

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given equation: $x e^{xy} = y + \sin^2 x$. Step $1$: Find the value of $y$ at $x = 0$. Substitute $x = 0$ into the equation: $0 \cdot e^{0} = y + \sin^2(0) \implies 0 = y + 0 \implies y = 0$. Step $2$: Differentiate both sides with respect to $x$ using the product rule and chain rule: $\frac{d}{dx}(x e^{xy}) = \frac{d}{dx}(y + \sin^2 x)$ $e^{xy} + x \cdot e^{xy} \cdot (y + x \frac{dy}{dx}) = \frac{dy}{dx} + 2 \sin x \cos x$. Step $3$: Substitute $x = 0$ and $y = 0$ into the differentiated equation: $e^{0} + 0 \cdot e^{0} \cdot (0 + 0 \cdot \frac{dy}{dx}) = \frac{dy}{dx} + 2 \sin(0) \cos(0)$ $1 + 0 = \frac{dy}{dx} + 0$ $\frac{dy}{dx} = 1$.

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

Similar Questions

If $x^y \cdot y^x = 16$,then $\frac{dy}{dx}$ at $(2, 2)$ is

The point which lies on the tangent drawn to the curve $x^4 e^y + 2 \sqrt{y+1} = 3$ at the point $(1,0)$ is

If $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,then $\frac{dy}{dx} = $

If $x^y=y^x$,then $x(x-y \log x) \frac{d y}{d x}$ is equal to :

If $x^{1/2} y^{1/3} = (x + y)^n$ and $x \frac{dy}{dx} - y = 0$, then $n =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module