Derivatives 1

$$-\frac{20}{x^5}$$  

$$\frac{20}{x^5}$$  

$$-\frac{20}{x^3}$$  

$$\frac{20}{x^3}$$  

$$\frac{dy}{dx}=3x^2-4x$$  

$$\frac{dy}{dx}=6x^{ }-4$$  

$$\frac{dy}{dx}=6x^2-4$$  

$$\frac{dy}{dx}=3x^2-4$$  

the slope of the tangent line

the slope of the normal line

the limit of a difference quotient

the derivative of the function  $$f\left(x\right)$$  with respect to  $$x$$  

$$\lim_{\Delta x\rightarrow0}\left(\frac{f\left(x+\Delta x\right)-f\left(x\right)}{\Delta x}\right)$$  

is the derivative

says to take the derivative of whatever follows

sin x

-cos x

-sin x cos x

-sin x

$$y\ '$$

$$\frac{d}{dx}$$

$$f'\left(x\right)$$

$$\frac{dy}{dx}$$

the slope of a tangent line

instantaneous rate of change

the tangent line

$$\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)$$