Explain why differentiating the equation with respect to produces the two terms and…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Explain why differentiating the equation

x^{2}y = 5

with respect to

x

produces the two terms

2xy

and

x^{2}\,\dfrac{dy}{dx}

on the left–hand side.

Related theory

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

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