If u, v and w are functions of x, then show that`d/(dx)(udotvdotw)=(d u)/(dx)vdotw+udot(d v)/(dx)dotw+udotv(d w)/(dx)`in two ways - first by repeated application of product rule, second by logarithmic differentiation.

If u, v and w are functions of x, then show that (d)/(dx) (u.v.w) = (du)/(dx) v.w + u.(dv)/(dx).w + u.v.(dw)/(dx) in two ways- first by repeated application of product rule, second by logarithmic differentiation. Using product rule

If y=(u)/(v) , where u and v are functions of x, show that v^(3)(d^(2)y)/(dx^(2))=|{:(u,v,0),(u',v',v),(u'',v'',2v'):}| .

(d)/(dx) (sin^(3)x) = …….

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

Differentiate the functions x^(sin x) + (sin x)^(cos x)

The function u=e^x sinx ; v=e^x cos x satisfy the equation v(d u)/(dx)-u(d v)/(dx)=u^2+v^2 b. (d^2u)/(dx^2)=2v c. (d^2)/(dx^2)=-2u d. (d u)/(dx)+(d v)/(dx)=2v