`(dy)/(dx)=(d)/(dx)(x+1)^6`

(d)/(dx)[sin^(4)(3x+1)]

If f(x)a n dg(x) a re differentiate functions, then show that f(x)+-g(x) are also differentiable such that d/(dx){f(x)+-g(x)}=d/(dx){f(x)}+-d/(dx){g(x)}

Using the first principle, prove that: d/(dx)(f(x)g(x))=f(x)d/(dx)(g(x))+g(x)d/(dx)(f(x))

Evaluate: (d)/(dx)((1)/(x))

Evaluate: (d)/(dx)((1)/(x^(3)))

(d)/(dx)(sin h^(-1)(3x))=

d/dx(x^n.logx)

Evaluate: (d)/(dx)(x^(1//2))

Evaluate: (d)/(dx)(x^(1//5))

Statement 1: If e^(xy)+ln(xy)+cos(xy)+5=0, then (dy)/(dx)=-y/x . Statement 2: d/(dx)(xy)=0,y is a function of x implies(dy)/(dx)=-y/x .