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← Everything for Calculus I
Calculus IDerivatives

Differentiation rules, one piece at a time.

Learn how to differentiate powers, exponentials, products and quotients. Then practise tangent lines, normal lines and motion, or type your own function.

Basic rules · Step 1 of 9

A fixed height has zero slope

−3−2−10123−1012345
A derivative tells you how fast a function changes as its input changes. A constant stays at the same height, so its graph is horizontal and its derivative is zero. The marks f′(x){f'(x)} mean the derivative of f.
Try it: Does a negative constant change when x changes?
ddx(c)=0{\displaystyle \frac{d}{dx}(c)} = {\displaystyle 0}

Even pi and e are constants. In the slope formula, the two heights cancel.

f′(x)=lim⁡h→0c−ch=0{\displaystyle f'(x)} = {\displaystyle \lim_{h\to0}\frac{c-c}{h}} = {\displaystyle 0}
Check yourself
What is the derivative of πe+7{\pi^e+7}?

Need a hand choosing the right derivative rule?

Bring your practice questions. We work through them together until every type feels routine.

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