If \(f(x)=\frac{x}{x+1}\), then its differential is given by

(a)

\(\frac { -1 }{ ({ x+1) }^{ 2 } } dx\)

(b)

\(\frac { 1 }{ ({ x+1) }^{ 2 } } dx\)

(c)

\(\frac { 1 }{ x+1 } dx\)

(d)

\(\frac {- 1 }{ x+1 } dx\)

If u(x, y) = x²+ 3xy + y - 2019, then \(\left.\frac{\partial u}{\partial x}\right|_{(4,-5)}\) is equal to

(a)

-4

(b)

-3

(c)

-7

(d)

13

Linear approximation for g(x) = cos x at \(x=\frac{\pi}{2}\) is

(a)

\(x+\frac{\pi}{2}\)

(b)

\(-x +\frac{\pi}{2}\)

(c)

\(x - \frac{\pi}{2}\)

(d)

\(-x - \frac{\pi}{2}\)

If w (x, y, z) = x² (y - z) + y² (z - x) + z²(x - y), then \(\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z } \) is

(a)

xy + yz + zx

(b)

x(y + z)

(c)

y(z + x)

(d)

0

If f(x,y, z) = xy +yz +zx, then f_x - f_z is equal to

(a)

z - x

(b)

y - z

(c)

x - z

(d)

y - x