Concept of the Derivative

Practice Questions

AP Calculus AB › Concept of the Derivative

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What is the derivative of ?

$\begin{align*}&\text{Calculate the limit of the difference quotient }f'(x)=\frac{f(x+h)-f(x)}{h}\&\text{For }f(x)=- x - 10\text{ as h approaches 0 for }x=-17\end{align*}$

$\begin{align*}&\text{The position of a particle at a given time is given by the function:}\&p(t)=6t - sin(\frac{(5\cdot \pi t)}{2}) + 5\&\text{What is its velocity at time }t=6\text{?}\end{align*}$

$\frac{\mathrm{d} }{\mathrm{d} x}(6x^2+8)=?$

What is the derivative of ?

$\begin{align*}&\text{The position of a particle at a given time is given by the function:}\&p(t)=6t - sin(\frac{(5\cdot \pi t)}{2}) + 5\&\text{What is its velocity at time }t=6\text{?}\end{align*}$

$\begin{align*}&\text{At any given time, a particle has the position :}\&p(t)=cos(4\cdot \pi t) - 2t - sin(2\cdot \pi t) - 3\&\text{Calculate its acceleration at time }t=4\end{align*}$

$\begin{align*}&\text{Calculate the limit of the difference quotient }f'(x)=\frac{f(x+h)-f(x)}{h}\&\text{For }f(x)=10x\text{ as h approaches 0.}\end{align*}$

$\begin{align*}&\text{At any given time, a particle has the position :}\&p(t)=cos(4\cdot \pi t) - 2t - sin(2\cdot \pi t) - 3\&\text{Calculate its acceleration at time }t=4\end{align*}$

What is the derivative of $2x^4+\frac{1}{2}x$ ?

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