(a) Define an explicit function and an implicit function. Give one example of each.…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

(a) Define an explicit function and an implicit function. Give one example of each. (b) List, in correct sequential order, the standard steps that are followed to obtain

\dfrac{dy}{dx}

when

y

is not given explicitly in terms of

x

. (c) The relation

x^2+xy+y^2=7

represents a curve in the

xy

–plane. Without carrying out any differentiation, explain why this relation must be handled as an implicit function of

x

while finding

\dfrac{dy}{dx}

for the curve.

Related theory

Advanced Differentiation
Implicit and Parametric Differentiation
Derivatives of implicit functions
Continuity and Differentiability

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