Derivative defined as the limit of the difference quotient

Practice Questions

AP Calculus AB › Derivative defined as the limit of the difference quotient

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

What is the derivative of ?

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

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

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

$\begin{align*}&\text{Calculate the limit of the difference quotient }f'(x)=\frac{f(x+h)-f(x)}{h}\&\text{For }f(x)=-8x\text{ as h approaches 0.}\end{align*}$

$\begin{align*}&\text{Calculate the limit of the difference quotient }f'(x)=\frac{f(x+h)-f(x)}{h}\&\text{For }f(x)=4x - 8x^{2} + 8\text{ as h approaches 0 for }x=19\end{align*}$

$\begin{align*}&\text{Calculate the limit of the difference quotient }f'(x)=\frac{f(x+h)-f(x)}{h}\&\text{For }f(x)=-7x\text{ as h approaches 0.}\end{align*}$

Find the derivative of the function using the limit of the difference quotient:

$\begin{align*}&\text{Calculate the limit of the difference quotient }f'(x)=\frac{f(x+h)-f(x)}{h}\&\text{For }f(x)=9 - 8x^{2} - 7x\text{ as h approaches 0 for }x=19\end{align*}$

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