Basic Differentiation Rules

 $f'\left(x\right)=6x^2+2$  

 $f'\left(x\right)=6x+2$  

 $f'\left(x\right)=6x^2+2$  

 $f'\left(x\right)=6x^2+2x^2-x$  

The slope of the secant line through c

The slope of the vertical line through c

The slope of the horizontal line through c

The slope of the line tangent to the function at c

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=x^{n-1}$

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=nx^{n-1}$

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{x^{n-1}}{n}$

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{n}{x^{n-1}}$

 $f'\left(x\right)=17x$  

 $f'\left(x\right)=17$  

 $f'\left(x\right)=0$  

 $f'\left(x\right)=17x^2$  

 $h'\left(x\right)=3$  

 $q'\left(x\right)=3$  

 $b'\left(x\right)=3$  

 $f'\left(x\right)=3$  

You can't take the derivative of 0.

0

This is all derivative.

Any constant

 $\frac{\partial y}{\partial x}=\frac{1}{x^4}$  

 $\frac{\partial y}{\partial x}=-3x$  

 $\frac{\partial y}{\partial x}=-\frac{3}{x^3}$  

 $\frac{\partial y}{\partial x}=-\frac{3}{x^4}$  

 $\frac{dy}{dx}=8x^7-12x^5-3x^2-4x$  

 $\frac{dy}{dx}=8x^7+12x^5-3x^2-4$  

 $\frac{dy}{dx}=8x^7+12x^5+3x^2+4x$  

 $\frac{dy}{dx}=8x^7-12x^5+3x^2+4$  

 $\frac{5}{2}x^{\frac{7}{2}}$  

 $\frac{5}{2}x^{\frac{1}{2}}$  

 $\frac{1}{2}x^{\frac{3}{2}}$  

 $\frac{5}{2}x^{\frac{3}{2}}$