Question

25. If y = x/(x+1) then dy/dx is :-​

Answer 1

Answer:

$\frac{1}{\left(x+1\right)^{2}}$

Explanation:

$\displaystyle\frac{d}{d x } \left( \frac{ x }{ x+1 } \right)$

$\frac{\left(x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+1)}{\left(x^{1}+1\right)^{2}}$

$\frac{\left(x^{1}+1\right)x^{1-1}-x^{1}x^{1-1}}{\left(x^{1}+1\right)^{2}}$

$\frac{x^{1}+x^{0}-x^{1}}{\left(x^{1}+1\right)^{2}}$

$\frac{\left(1-1\right)x^{1}+x^{0}}{\left(x^{1}+1\right)^{2}}$

$\frac{1}{\left(x+1\right)^{2}}$