For , where , answer the…

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For

y=\ln (5x+2)

, where

x>-\dfrac{2}{5}

, answer the following: (i) Calculate

\dfrac{dy}{dx}

. (ii) Determine

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

. (iii) Find the numerical value of

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

x=1

Related theory

Higher-Order Derivatives
Advanced Differentiation
Derivatives of standard functions via chain rule
Exponential and logarithmic functions
Continuity and Differentiability

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