Let the derivative of be defined as

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

Problem

Let the derivative of f(x)f(x) be defined as D∗f(x)=lim⁡h→0f2(x+h)−f2(x)hD^* f(x) = \lim_{h \to 0} \frac{f^2(x+h) - f^2(x)}{h} , where f2(x)={f(x)}2f^2(x) = \{f(x)\} ^2 . If u=f(x)u = f(x) , v=g(x)v = g(x) , then the value of D∗(uv)D^*\left(\frac{u}{v}\right) is (1) u2(D∗v)−v2(D∗u)v4\frac{u^2(D^*v) - v^2(D^*u)}{v^4} (2) u(D∗v)−v(D∗u)v2\frac{u(D^*v) - v(D^*u)}{v^2} (3) v2(D∗u)−u2(D∗v)v4\frac{v^2(D^*u) - u^2(D^*v)}{v^4} (4) v(D∗u)−u(D∗v)v2\frac{v(D^*u) - u(D^*v)}{v^2}

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