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Basic Derivative Formulas Calculator

Elementary derivative lookup. Built-in power, exponential, log and trig functions—choose one, enter parameters and x to get the derivative formula and value—for memorizing rules.

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(x^n)′=n·x^(n−1) (e^x)′=e^x (ln x)′=1/x
Basic elementary function
n for power; base a for a^x/log_a x; ignored otherwise
Compute the derivative here

📖 Tutorial｜Basic Derivative Formulas

1. Definition
Basic elementary functions have fixed derivative formulas for powers, exponentials, logs and trig functions—the foundation of all differentiation.
2. Symbols
FunctionDerivative
x^nn·x^(n−1)
e^xe^x
a^xa^x·ln a
ln x1/x
sin xcos x
cos x−sin x
3. How it works
  • The tool applies the analytic formula for the chosen function;
  • Then substitutes x numerically;
  • The parameter n or base a is used only where relevant.
4. Steps
  1. Choose the function type;
  2. Fill the parameter (n for power, base a for exp/log);
  3. Enter x and click Calculate.
5. Example
Example: x^2 at x=3. (x²)′=2x, so at x=3 the value is 6.
6. Pitfalls
Power rule: bring the exponent down and decrement it;
Do not forget ln a in (a^x)′;
(ln x)′=1/x while (log_a x)′=1/(x ln a).

❓ FAQ｜Basic Derivative Formulas

What is the power rule?
(x^n)′ = n·x^(n−1). E.g. (x²)′=2x, (x³)′=3x².
Why is the derivative of e^x itself?
e is defined so that (e^x)′=e^x, a special property of exponentials.
How does (a^x)′ differ from (e^x)′?
(a^x)′=a^x·ln a adds a factor ln a; when a=e, ln e=1 and it reduces to e^x.
Why does the log derivative carry 1/x?
(ln x)′=1/x is a basic result derived from the definition and important limits.
Which trig derivatives to memorize?
(sin x)′=cos x, (cos x)′=−sin x, (tan x)′=sec²x.