Derivatives Calculator

Enter the expression and variable for which to differentiate. Use * to indicate multiplication between coefficients and variables. For example, enter 2*x^2+3*x^(-1)+2, instead of 2x^2+3x^(-1)+2.



Solution:

Examples:

  • To derive \(f(x)=2x^2+3x-2\), enter 2*x^2+3*x-2 and the variable x.
  • To derive \(f(t)=\frac{1}{3}t^2+\frac{4}{3}t\), enter 1/3*t^2+4/3*t and the variable t.
  • To derive \(f(x)=\frac{1}{2*x}+\frac{1}{3x^2}\), enter 1/(2*x)+1/(3*x^2) and the variable x.

With this calculator, you can get the derivative of the expression entered. It is possible to find derivatives of polynomials, trigonometric functions, exponential functions, among others. The expression must be entered along with the variable for which to derive.

How to use the derivatives calculator?

Step 1: Enter the expression to be derived in the first input box. Use * to indicate multiplication between variables and coefficients. For example, instead of entering 2x or 5x^2, enter 2*x or 5*x^2.

Step 2: Enter the variable for which to derive in the second input box. In most cases, the variable is x.

Step 3: Click “Derive” to get the derivative of the entered expression.

Step4: The derivative along with the original expression will be displayed at the bottom.

How to enter expressions in the calculator?

To enter expressions, we just have to enter an expression without the equals sign. For example, if we want to derive the function f(x)=x+2, we just have to enter x+2.

Also, we must use the * sign to indicate multiplication between variables and coefficients and the ^ sign to indicate an exponent. Therefore, to input the expression \(2x^2+3x\), we need to enter 2*x^2+3*x.

Lastly, we can enter fractions by using the / sign. To input \(\frac{1}{2}x^2+\frac{1}{3}x\), we would type 1/2*x^2+1/3*x. The following are some examples of how to use the calculator.

  • To derive \(g(x)=3x^2+2x-4\), enter 3*x^2+2*x-4 and the variable x.
  • To derive \(f(x)=\frac{1}{2}x^2+\frac{4}{3}x\), enter 1/2*x^2+4/3*x and the variable x.
  • To derive \(h(t)=\frac{1}{2*t}+\frac{1}{3t^2}\), enter 1/(2*t)+1/(3*t^2) and the variable t.

Why find derivatives?

Derivatives have many applications in mathematics, some of the most important are:

  • We can find the rate of change of a quantity. This is generally the most important application of the derivative. For example, we can find the rate of change of the volume of a sphere with respect to the change in radius.
  • We can determine increasing and decreasing functions. The derivative can tell us whether a function is increasing or decreasing at a certain point.
  • The derivative also allows us to find the tangent to a curve.
  • Maximum points, minimum points, and other inflection points can be found using the derivative.

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