FANDOM


A derivative of a function is a second function showing the rate of change of the dependent variable compared to the independent variable. It can be thought of as a graph of the slope of the function from which it is derived. The process of finding a derivative is called differentiation.

Definition
Let D\subseteq\R and f:D\to\R be a function. Then the derivative of f is a function f':D'\to\R defined by:
f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}.

The derivative is undefined when this limit does not exist, that is, f is not differentiable.

Properties

See also: Derivative formulas

A simpler way of finding the derivative is to multiply the coefficient by the exponent and subtract one from the exponent (proof). For example:

(x^r)'=rx^{r-1}

The function

f(x)=5x^3+2x^2+4x+6

can be differentiated as follows:

\begin{align}f(x)&=5x^3+2x^2+4x+6\\
f'(x)&=(3)5x^{3-1}+(2)2x^{2-1}+(1)4x^{1-1}+(0)6\\
&=15x^2+4x^1+4x^0+0\\
&=15x^2+4x+4\end{align}

In graphs, the derivative of a function f at a number a is equal to the slope of the tangent line of the graph of f at the point (a,f(a)) .

See also

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.