After differentiating the equation implicitly

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

Problem

After differentiating the equation

x^{2}+y^{2}=25

implicitly, a student obtained

\frac{dy}{dx}=\frac{-2x}{2y}.

Using this (unsimplified) form of

\dfrac{dy}{dx}

, what is the value of

\displaystyle\frac{d^{2}y}{dx^{2}}

at the point

(4,3)

on the curve? (a)

-\dfrac{25}{9}

(b)

\dfrac{25}{27}

(c)

-\dfrac{25}{27}

(d)

-\dfrac{27}{25}