People living at Mars define the derivative of in an unusual manner as where denotes…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

People living at Mars define the derivative of

f(x)

in an unusual manner as

D^*f(x)=\lim_{h\to 0}\frac{f^2(x+h)-f^2(x)}{h}

where

D^*f(x)

denotes the derivative of

f(x)

at Mars. If

u=f(x), v=g(x)

, then

D^*(uv)

is (a)

(D^*u)v+(D^*v)u

(b)

u^2D^*v+v^2D^*u

(c)

D^*u+D^*v

(d)

uvD^*(u+v)