[" If "y=f(u)" is a differentiable function of u and "u=g(x)" is differentiate function of "x" such that the "],[" composite function "y=f[g(x)]" is differentiable function of "x" then "(dy)/(dx)=(dy)/(du)times(du)/(dx)" ."]

If y = f(u) is a differentiable functions of u and u = g(x) is a differentiable functions of x such that the composite functions y = f[g(x) ] is a differentiable functions of x then (dy)/(dx) = (dy)/(du) . (du)/(dx) Hence find (dy)/(dx) if y = sin ^(2)x

If y =f(u) is differentiable function of u, and u=g(x) is a differentiable function of x, then prove that y= f [g(x)] is a differentiable function of x and (dy)/(dx)=(dy)/(du)xx(du)/(dx) .

Prove that (d)/(dx)uv=u(dv)/(dx)+v(du)/(dx) .

If x=f(t) and y=g(t) are differentiable functions of t then (d^(2)y)/(dx^(2)) is

Differentiate the function log_(x)5

If x=f(t) and yy=g(t) are differentiable functions of t then (d^(2)y)/(dx^(2)) is

Differentiate the function (log x)^(cos x)

The function y = cx is the solution of differential equation (dy)/(dx) = (y)/(x)

Differentiate the function sin (2x-3) .