If x = r cos θ, y = r sin, then \(\frac { \partial r }{ \partial x } \) = ....................

If u = sin-1 \(\left( \frac { { x }^{ 4 }+{ y }^{ 4 } }{ { x }^{ 2 }+{ y }^{ 2 } } \right) \) and f = sin u then f is a homogeneous function of degree ..................

If u = y^x then \(\frac { \partial u }{ \partial y } \) = ............

If y = sin x and x changes from \(\frac{\pi}{2}\) to ㅠ the approximate change in y is ..............

The cube root of 127 is ............

The approximate value of (627)^\(\frac14\) is ................

If f(x, y) = 2x² - 3xy + 5y + 7 then f(0, 0) and f(1, 1) is _____________

If f (x, y) = x³ + y³ - 3xy² then \(\frac { { \partial }f }{ \partial { x } } \) at x = 2,_____________

If u = log (x³ + y³ + z³ - 3xyz) then \(\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z } \) = _____________

If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then f_xx is _____________

lf u = (x-y)⁴+(y-z)⁴ +(z-x)⁴ then \(\sum { \frac { \partial u }{ \partial x } } \) = _____________

If u = x^y + y^x then u_x + u_y at x = y = 1 is _____________

If u = log \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \), then \(\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } } \) is _____________

If the radius of the sphere is measured as 9 cm with an error of 0.03 cm, the approximate error in calculating its volume is _____________

If y = x⁴ - 10 and if x changes from 2 to 1.99, the approximate change in y is ________