<derivative>

<derivative> is a Math component that renders the derivative of basic elementary functions (including polynomial, exponential, and trigonometric functions.)

Attributes and Properties

Example: <derivative> of a nested function

A <derivative> renders the derivative of the enclosed math expression, if the expression can be interpreted as a function in $x$.

Example: <derivative> of a named function

A <derivative> renders the derivative of the named <function>.

Example: <derivative> of a function of a different variable

A <derivative> renders the derivative of the named <function>. The <function> is defined in terms of $y$ with the variables attribute and this information is carried over when evaluating the derivative.

Example: Partial derivatives

A <derivative> renders the derivative of the named <function>. The <function> is defined in terms of $x$ and $z$ with the variables attribute. The variable for differentiation of the partial derivative is specified with the derivVariables attribute.

Example: Higher-order derivatives

Higher-order derivatives can be rendered by entering multiple values in the derivVariables attribute.

Attribute Example: derivVariables

<p><m>h(y,z) = </m>
<function name="h" variables="y z">
  y z^2 + 2z cos(y)
</function>
</p>
 
<p><m>\frac{\partial h}{\partial y} = </m>
  <derivative derivVariables="y">
    $h
  </derivative>
</p>
 
<p><m>\frac{\partial h}{\partial z} = </m>
  <derivative derivVariables="z">
    $h
  </derivative>
</p>
 
<p><m>\frac{\partial^2 h}{\partial z \partial y} = </m>
  <derivative derivVariables="z y">
    $h
  </derivative>
</p>

The derivVariables attribute specifies the variable of differentiation (or a list of variables to differentiate with respect to) for multivariable functions.

Attribute Example: variables

<p><m>\frac{d}{dt}( x \cos(t)) = </m>
  <derivative variables="t">
    x cos(t)
  </derivative>
</p>

The variables attribute can be used to specify the function variable if not specified by <function> definition.

Property Example: nInputs

<p><m>\frac{\partial f}{\partial x}( x \cos(t)) = </m>
  <derivative variables="x t" derivVariables="x" name="fPrime">
    x cos(t)
  </derivative>
</p>
 
<p><c>numInputs</c> = $fPrime.numInputs</p>

The numInputs property returns the number of inputs associated with the enclosed function.

Property Example: numDerivatives

<p><m>\frac{\partial}{\partial t} \bigg(
  \frac{\partial^2 f }{\partial x^2}
  ( x^2 \cos t)\bigg) = </m>
  <derivative variables="x t" 
    derivVariables="x x t" name="fPrime">
    x^2 cos(t)
  </derivative>
</p>
 
<p><c>numDerivatives</c> = $fPrime.numDerivatives</p>

The numDerivatives property returns the number of differentiations performed on the enclosed function.

Example: attributes as properties

Both attributes of the <derivative> component are also accessible as properties.