For assistance computing the derivative f '(x), try the Derivative Calculator.
Polynomial f (x)=x^{3}+2x^{2}-3x+1 f '(x)=3x^{2}+4x-3 |
Exponential f (x)=e^{x} f '(x)=e^{x} |
Trigonometric f (x)=sin(x) f '(x)=cos(x) | ||
Product Rule f (x)=x sin(x) f '(x)=x cos(x) + sin(x) |
Chain Rule f (x)=e^{-x2} f '(x)=-2xe^{-x2} |
Incorrect f (x)=e^{x} f '(x)=xe^{x-1} (Improper use of Power Rule) |
Since the graphing procedures do not attempt to check the calculus computation of f '(x), the graph can show the visual consequences of incorrect calculations, as in the incorrect example above.
However, this also allows the graphing procedures to produce visual effects other than tangent lines. For example, using the slope m=-1/f '(x) gives lines normal to the graph of the function f (x), an effect which can be achieved in the graph by entering this m expression into the text input field marked "f '(x)=" (Example: f (x)=e^{x}, m=-e^{-x}).