MCQ
If $x^py^q=(x+y)^{p+q}$,then $\frac {dy}{dx}=$
- ✓$\frac {y}{x}$
- B$-\frac {y}{x}$
- C$\frac {x}{y}$
- D$-\frac {x}{y}$
$\Rightarrow m \ln x+n \ln y=(m+n) \ln (x+y)$
Differentiating both sides.
$\therefore \frac{m}{x}+\frac{n}{y} \frac{d y}{d x}=\frac{m+n}{x+y}\left(1+\frac{d y}{d x}\right)$
$\Rightarrow\left(\frac{m}{x}-\frac{m+n}{x+y}\right)=\left(\frac{m+n}{x+y}-\frac{n}{y}\right) \frac{d y}{d x}$
$\Rightarrow \frac{m y-n x}{x(x+y)}=\left(\frac{m y-n x}{y(x+y)}\right) \frac{d y}{d x}$
$\Rightarrow \frac{d y}{d x}=\frac{y}{x}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
($A$) differentiable at $x=0$ if $a=0$ and $b=1$
($B$) differentiable at $x=1$ if $a=1$ and $b=0$
($C$) $NOT$ differentiable at $x=0$ if $a=1$ and $b=0$
($D$) $NOT$ differentiable at $x=1$ if $a=1$ and $b=1$