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This online calculator is currently under heavy development. It may or it may NOT work correctly.
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Various forms of function formulas
Name  Formula  Legend 
Exponential function in general form  Show source$y={ a}^{ x}$ 

Exponential function with base e (often written as exp(x))  Show source$exp(x)={ e}^{ x}$ 

Homographic function in general form  Show source$y=\frac{ a~ x+ b}{ c~ x+ d}$ 

Function b/x  Show source$y=\frac{ b}{ x}$ 

Linear function in slopeintercept form  Show source$y= a~ x+ b$ 

Linear function in pointslope form  Show source$y=\mathrm{a}\left( x x_0\right)+ y_0$ 

Linear function in constantslope form  Show source$\frac{y  y_0}{x  x_0} = \frac{y_1  y_0}{x_1  x_0}$ 

Zero of the linear function from constantslope form  Show source$x=\frac{ y_0\cdot\left( x_1 x_0\right)}{ y_1 y_0}+ x_0$ 

Quadratic function in standard form  Show source$y= a~{ x}^{2}+ b~ x+ c$ 

Quadratic function in factored form  Show source$y=\mathrm{a}\left( x x_1\right)~\left( x x_2\right)$ 

Quadratic function in vertex form  Show source$y={\mathrm{a}\left( x h\right)}^{2}+ k$ 

Function properties
Name  Formula  Legend 
Product of two exponential functions  Show source$a ^ {x} \cdot a ^ {y} = a ^ {x + y}$ 

Quotient of two exponential functions  Show source$\frac{a ^ {x}}{a ^ {y}} = a ^ {x  y}$ 

Derivatives and integrals
Name  Formula  Legend 
Derivative of general exponential function  Show source$\frac{d}{d x} a^{x} = a^{x} \ln(a)$ 

Derivative of exponential function with e base, derivative of exp(x) function  Show source$\frac{d}{d x} e^{x} = e^{x} \ln(e) = e^{x}$ 

Indefinite integral of general exponential function  Show source$\int a^{x} dx = \frac{a^{x}}{\ln(a)}$ 

Indefinite integral of exponential function with e base, integral of exp(x) function  Show source$\int e^{x} dx = e^{x}$ 

Some facts
 Exponential function is a function that can be presented in the form:
$y={ a}^{ x}$where:
 $y$  function value (the function value at single point x, often marked as f(x)),
 $x$  function argument (called also independent value),
 $a$  base of the exponential function.
 A special case is the exponential function of the base e (→ see the number e):
$exp(x)={ e}^{ x}$  The exponential function with the base e is often denoted as exp (x), which we read as exponent of x.
 The inverse function for the exponential one is logarithmic function. In particular for the function exp(x) (the base is number e) the inverse function is natural logarithm.
 The exponential function has no zero poins. Its all values are located above the OX axis (all function values are positive).
 Depending on the base a, we can distinguish three scenarios:
 base is less than one (a <1)  function is decreasing,
 base is greater than one (a > 1)  the function is inreasing,
 base is equal to zero (a = 0)  the function is reduced to constant function.
 base is less than one (a <1)  function is decreasing,
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exponential_function · exponent · e_to_x · exp_x · a_to_x · math_tables_exponential_function · exponential_function_formulas · exponential_asymptotes_formulas · properties_of_exponential_function · expx_formula · exponens_formula
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