Explain why differentiating with respect to (where is a differentiable function of )…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Explain why differentiating

\sec y

with respect to

x

(where

y

is a differentiable function of

x

) necessarily introduces the factor

\dfrac{dy}{dx}

in the result.

Related theory

Differentiation Rules
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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