# How do you take a derivative with respect to time?

## How do you take a derivative with respect to time?

Derivatives with respect to time

1. Velocity is the derivative of position with respect to time: v(t)=ddt(x(t)).
2. Acceleration is the derivative of velocity with respect to time: a(t)=ddt(v(t))=d2dt2(x(t)).

## How do you differentiate in Matlab?

Differentiation

1. syms x f = sin(5*x); The command.
2. diff(f) differentiates f with respect to x :
3. ans = 5*cos(5*x) As another example, let.
4. g = exp(x)*cos(x);
5. y = exp(x)*cos(x) – exp(x)*sin(x)
6. ans = -9.7937820180676088383807818261614.
7. ans = -2*exp(x)*sin(x)
8. ans = -2*exp(x)*sin(x)

How do you differentiate an array in Matlab?

Y = diff( X ) calculates differences between adjacent elements of X along the first array dimension whose size does not equal 1: If X is a vector of length m , then Y = diff(X) returns a vector of length m-1 . The elements of Y are the differences between adjacent elements of X .

### How do you plot a derivative in Matlab?

1. Call polyfit to generate your polynomial (if you don’t already have a polynomial)
2. Call polyder to get derivative of your fitted line.
3. Call polyval with your original X values to get the Y values of your derivative and plot that with hold on so it doesn’t erase your original plot.

### Why do we differentiate with respect to time?

For example if you are given the displacement an object as a function of time and you want to know its velocity at a particular point of time, you need to find the derivative of the displacement function with respect to time to get velocity as a function of time (because velocity is the rate of change of displacement …

What is the rate of change with respect to time?

Velocity is the rate of change of distance with respect to time.

#### What does Syms mean in MATLAB?

symbolic object
The syms function creates a symbolic object that is automatically assigned to a MATLAB® variable with the same name. The sym function refers to a symbolic object that can be assigned to a MATLAB variable with the same name or a different name.

#### What is difference between vector and matrix in MATLAB?

In MATLAB terminology, both vectors and matrices are arrays of numerical values. Technically, a vector is a form of a matrix having one row or one column (read about isvector and ismatrix commands for more information). Vectors are a subclass of matrices, so every vector is a matrix.

How does Matlab calculate dy dx?

Use diff and == to represent differential equations. For example, diff(y,x) == y represents the equation dy/dx = y. Solve a system of differential equations by specifying eqn as a vector of those equations. S = dsolve( eqn , cond ) solves eqn with the initial or boundary condition cond .

## How to differentiate a symbolic expression in MATLAB?

Df = diff (f) differentiates f with respect to the symbolic variable determined by symvar (f,1). Df = diff (f,n) computes the n th derivative of f with respect to the symbolic variable determined by symvar.

## How to differentiate a multivariate expression in MATLAB?

If you differentiate a multivariate expression or function F without specifying the differentiation variable, then a nested call to diff and diff (F,n) can return different results. This is because in a nested call, each differentiation step determines and uses its own differentiation variable.

How to determine the default variable in MATLAB?

To determine the default variable that MATLAB differentiates with respect to, use symvar: Calculate the second derivative of f with respect to t: Note that diff (f, 2) returns the same answer because t is the default variable. To further illustrate the diff command, define a, b, x, n, t , and theta in the MATLAB workspace by entering

### Can you find the derivative of G twice in MATLAB?

Find the derivative of g at x = 2. You can get the same result by taking the derivative twice: In this example, MATLAB ® software automatically simplifies the answer. However, in some cases, MATLAB might not simplify an answer, in which case you can use the simplify command.