Question

The slope of the tangent to the curve $y^2{e}^{xy}=9e^{-3}{x}^2$ at $(-1,3)$ is

• A. $\frac{-15}{2}$
• B. $\frac{-9}{2}$
• C. $15$
• D. $\frac{15}{2}$
• E. $\frac{9}{2}$

Answer 1

The correct option is C $15$

Given curve: $y^2{e}^{xy}=9e^{-3}{x}^2$

Differentiating it wrt $x$,we get

$2y{e}^{xy}\frac{dy}{dx}+y^2{e}^{xy}(y+x\frac{dy}{dx})=18e^{-3}x$

Putting $x=-1$ and $=3$ in above equation,

$2\times 3\times e^{-3}\frac{dy}{dx}+3^2{e}^{-3}(3-1\frac{dy}{dx})=18e^{-3}\times (-1)$

$\Rightarrow 6\frac{dy}{dx}+27-9\frac{dy}{dx}=-18$

$\Rightarrow -3\frac{dy}{dx}=-45$

$\Rightarrow \frac{dy}{dx}=15$

Hence, C is the correct option.