NDA 2015
- Exam
- NDA
- Year
- 2015
- Subject
- Mathematics
- Chapter
- Differentiation
NDA 2015 · Mathematics · Differentiation
If x^a y^b=(x-y)^ a+b , then the value of (d y)/(d x)-(y)/(x) is...
If , then the value of is equal to
Options
- A
- B
- C1
- D0
Correct answer
D. 0
Step-by-step solution
taking log both the sides.
\begin{aligned}
& \log \left(x^a y^b\right)=\log (x-y)^{(a+b)} \\
& \text{ a \log x }+b \operatorname{\log y}=(a+b) \log (x-y) \\
& \text{ differentiating both sides w.r. }{ }^{\prime} x^{\prime} . \\
& \frac{a}{x}+\frac{b}{y} \frac{d y}{d x}=\frac{(a+b)}{(x-y)}\left[1-\frac{d y}{d x}\right] \\
& \frac{d y}{d x}\left[\frac{b}{y}+\frac{a+b}{x-y}\right]=\frac{a+b}{x-y}-\frac{a}{x} \\
& \frac{d y}{d x}\left[\frac{b x-b y+a y+b y}{y(x-y)}\right]=\frac{a x+b x-a x+}{x(x-y)} \\
& \frac{d y}{d x}\left[\frac{b x+a y}{y}\right]=\frac{b x+a y}{x} \\
& \frac{d y}{d x}=\frac{y}{x} \\
& \frac{d y}{d x}-\frac{y}{x}=0
\end{aligned}