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

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

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 the value of

D^*\left(\frac{u}{v}\right)

is (a)

\frac{u^2D^*v-v^2D^*u}{v^4}

(b)

\frac{uD^*v-vD^*u}{v^2}

(c)

\frac{v^2D^*u-u^2D^*v}{v^4}

(d)

\frac{vD^*u-uD^*v}{v^2}

Related theory

Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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