composite

Examples of composite in the following topics:

• The Chain Rule

  • The chain rule is a formula for computing the derivative of the composition of two or more functions.
  • The chain rule is a formula for computing the derivative of the composition of two or more functions.
  • That is, if $f$ is a function and $g$ is a function, then the chain rule expresses the derivative of the composite function $f \circ g$ in terms of the derivatives of $f$ and $g$.
  • Calculate the derivative of a composition of functions using the chain rule

• Numerical Integration

  • This is called a composite rule, extended rule, or iterated rule.
  • For example, the composite trapezoidal rule can be stated as

• The Chain Rule

  • The chain rule is a formula for computing the derivative of the composition of two or more functions.
  • That is, if $f$ is a function and $g$ is a function, then the chain rule expresses the derivative of the composite function $f \circ g (x) ≡ f [g (x)]$ in terms of the derivatives of $f$ and $g$.

• Numerical Integration

  • This is called a composite rule, extended rule, or iterated rule.
  • For example, the composite trapezoidal rule can be stated as:

• Fundamental Theorem for Line Integrals

  • If $\varphi$ is a differentiable function from some open subset $U$ (of $R^n$) to $R$, and if $r$ is a differentiable function from some closed interval $[a,b]$ to $U$, then by the multivariate chain rule, the composite function $\circ r$ is differentiable on $(a,b)$ and $\frac{d}{dt}(\varphi \circ \mathbf{r})(t)=\nabla \varphi(\mathbf{r}(t)) \cdot \mathbf{r}'(t)$ for for all $t$ in $(a,b)$.