AP Calculus AB 2.6 Derivative Rules Question Bank

Practise AP Calculus AB 2.6 questions using linearity to differentiate constants, sums, differences and constant multiples.

Exam points

differentiate sums and differences term by term
apply constant and constant-multiple derivative rules

Covered syllabus points

FUN-3.A—Calculate derivatives of familiar functions—Topic 2.6

[Maximum number: 1]

Let be the function defined by $f(x)=b x^{2}+3 b x+b^{2}+\frac{1}{x^{2}}$ , where b is a nonzero constant. Which of the following is an expression for $f^{\prime}(x)$ , the derivative of f(x) ?

$2 b x+3 b-\frac{2}{x}$

$2 b x+3 b-\frac{2}{x^{3}}$

$2 b x+3 b+b^{2}-\frac{2}{x^{3}}$

$x^{2}+3 x+2 b$

g(x)=\left\{\begin{array}{lll} x^{2}+1 & \text { for } & x<3 \\ 13-x & \text { for } & x \geq 3 \end{array}\right.

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Covered syllabus points

2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple question 1