" (iv) "3^(u(x))

Find the derivatives w.r.t. x : 3^(u(x))

Find the derivatives of the following functions w.r.t x (or u): (u^(3)+3^(u))"cosecu"

If u = sin ^(-1) ((x ^(3) + y ^3)/(x-y)) show that x (del u)/(delx) + y (del u )/(del y) = 2 tan u.

If U(x,y,z) = log(x^(3) + y^(3) +z^(3)) find (del U)/(dx) + (del U)/(dy) + (del U)/(dz)

A particle moving in a straight line is acted upon by a force which works at a constant rate and chages ist melocity from (u and v ) over a distance x. Prove that the taken in it is 3/2 (u+v)x/(u^(2)+v^(2)+uv) .

A particle moving in a straight line is acted upon by a force which works at a constant rate and changes its velocity from (u and v ) over a distance x. Prove that the taken in it is 3/2 (u+v)x/(u^(2)+v^(2)+uv) .

If u = x^(4) + y ^(3) + 3x ^(2) y^(2) + 3x ^(2) y find (del u)/(delx), (delu)/(dely), (del^(2) u)/(delx^(2)) , (del^(2)u)/(delx dely).

If u = log ((x ^ (2) + y ^ (2)) / (x + y)), prove that x (u) / (x) + y (u) / (y) = 1