# Tangent Line Equation Calculator



A step by step tangent line equation calculator is presented.

## Equation of the Tangent Line

Let $f(x)$ be a function. The slope $m$ of the tangent line to the graph of $f(x)$ at the point of tangency $(x_0 , f(x_0))$ is given by:
$m = f'(x_0)$
where $f'(x_0)$ is the first derivative of $f(x)$ evaluated to $x = x_0$
The equation of the tangent to the graph of $f(x)$ at $x = x_0$ in point slope form is given by
$y - f(x_0) = m(x - x_0)$
and in slope intercept form is given by
$y = m x + f(x_0) - m x_0$
You enter $f(x)$ and $x_0$ and the calculator displays the point of tangency $( x_0 , f(x_0) )$, the slope $m$ and the equation of the line in slope intercept form $y = m x + b$ with the y intercept $b = f(x_0) - m x_0$.

## Use of the Tangent Line Calculator

1 - Enter and edit function $f(x)$ and click "Enter Function" then check what you have entered. Enter $x_0$
Note that the five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = x^3 + 1/x.(more notes on editing functions are located below)
2 - Click "Calculate Equations".
3 - Note that the natural logarirthm is entered as $log(x)$, the natural exponential as   $exp(x)$.
4 - Note that a function $f(x)$ to some power $n$ is entered as: $(f(x))^n$. Example:   $sin^2(2x-1)$   is entered as   (sin(2x-1))^2.
5 - Note Enter decimal numbers as fractions between brackets. Example : enter (1/2) instead of 0.5

$f(x)$ =

$x_0$ =

Number of Decimals =

Notes: In editing functions, use the following:
1 - The five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example:    f(x) = x^2 + 1/x + log(x)  )
2 - The function square root function is written as (sqrt). (example: sqrt(x^2-1) for $\sqrt {x^2 - 1}$ )
3 - The exponential function is written as exp(x). (Example: exp(x+2)    for    $e^{x+2}$ )
4 - The log base e function is written as log(x). (Example: log(x^2-2)    for    $\ln(x^2 - 2$ )
Here are some examples of functions that you may copy and paste to practice:
x^2 + x +2       sin(x) + cos(x)       1/(x-2)       x^2+log(2*x + 2)      (x+2)^2(x^2+1)-1
2*sin(2x^2+2x-1)       exp(2x^2)       tan(x)       (x-1)/(x+3)^3