Consider the circle .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Consider the circle

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

. (i) Determine

\dfrac{dy}{dx}

in terms of

x

and

y

. (ii) Hence find

\dfrac{d^{2}y}{dx^{2}}

in terms of

x

and

y

. (iii) Evaluate

\dfrac{d^{2}y}{dx^{2}}

at the point

(3,4)

on the circle.

Related theory

Higher-Order Derivatives
Advanced Differentiation
Implicit and parametric differentiation
Derivatives of implicit functions
Continuity and Differentiability

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