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

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

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

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

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

If \(g(x, y)=3 x^{2}-5 y+2 y^{2}, x(t)=e^{t}\) and y(t) = cos t, then \(\frac{dg}{dt}\) is equal to

The approximate change in the volume V of a cube of side x metres caused by increasing the side by 1% is

The change in the surface area S = 6x² of a cube when the edge length varies from x_o to x_o+ dx is

If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is

If f (x, y) = e^xy then \(\frac { { \partial }^{ 2 }f }{ \partial x\partial y } \) is equal to

If w (x, y) = x^y, x > 0, then \(\frac { \partial w }{ \partial x } \) is equal to

If v (x, y) = log (e^x + e^y), then \(\frac { { \partial }v }{ \partial x } +\frac { \partial v }{ \partial y } \) is equal to

If \(u(x, y)=e^{x^{2}+y^{2}}\),then \(\frac { \partial u }{ \partial x } \) is equal to

The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is