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.

D^*(\tan x)

is equal to (a)

\sec^2 x

(b)

2\sec^2 x

(c)

\tan x\sec^2 x

(d)

2\tan x\sec^2 x

Related theory

Derivative Foundations
Differentiation Rules
Rules of differentiation
Derivatives
Limits and Derivatives

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