Let . Differentiate and explain in one sentence why substituting and into gives the…

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

Problem

Let

E(x)=e^{x^{2}}

. Differentiate

E

and explain in one sentence why substituting

x=3

and

x=1

into

E

gives the exact value of

\displaystyle \int_{1}^{3} 2x\,e^{x^{2}}\,dx

Related theory

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

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