For the curve defined by and ( )

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

Problem

For the curve defined by

x=e^{3t}

and

y=\ln t+e^{t}

(

t>0

), find

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

t=1

. Hence state whether the curve is concave upward or concave downward at that point.

Related theory

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

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