Consider the function defined for all real .

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

Problem

Consider the function

f(x)=3\cdot 2^{x}+5\,e^{x}

defined for all real

x

. (i) Find

f'(x)

. (ii) Find

f''(x)

. (iii) Hence, calculate

f''(0)

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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