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Derivative of a Function Calculator

Solution to any derivative of a function of x
For example: 2x³ + 12x² + 12x +5
using Geogebra

Why it is important to learn how to compute the derivative of a function? Derivative is one of the subjects taught in Calculus.

Answer

The derivative of a function of any real number variable measures the sensitivity to change of the function value (function value meaning output value or the y-axis ) with respect to a change in its argument (argument meaning input value or the x - axis). The derivative of a function is also known as the slope at instantaneous moment of time or snapshot of time. The derivative of a function is also called the rate of change. You can acquire knowledge how to compute the derivative or rate of change by studying Calculus. For example, the derivative of the distance (output value or the y-axis) of a moving object with respect to time ( input value or the x-axis) is the object's velocity ( v = d/t ): this measures how quickly the position of the object changes when time advances.

Finding the slope of a curve graph or function is also called finding the derivative of the curve. In straight line , finding the slope of a line is easy. Just remember the line equation written in slope form which is y = m x + b ; where the letter m represents the slope of a line and it is always constant value. For example when m = 4, it means in a straight line the slope is always constant m = 4. For a curve line we use the derivative to find the value of slope . It is a function because the slope is not constant. For example you have a parabolic function given by the equation y = x ², the calculated slope or first derivative also called y prime ( y ^' ) is equal to 2x, it keeps changing depending on the value of x along the curve.

So given a parabolic curve equation y = x ² , Find the slope function or the derivative of
y = x ² . Answer the slope ( y ^' ) = 2 x . It means at instant the value of x = 1 , the slope y ^' = 2. In Calculus , y - prime is written as y ^' . It tells you that it is the calculated slope at a snapshot value of x or at the instantaneous value of x, like when x = 1. Imagine you have the power to freeze time at 1 second what is the value of the slope? That's why learning Calculus tool like derivative or rate of change or slope is interesting because it gives you the imagination to freeze time and find the position of an object moving forward or backward in timeline or along any point in x - axis.

By Apolinario "Sam" Ortega, 07 August 2016, Created with GeoGebra

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Using Wolfram Alpha to compute derivative or slope at snapshot value of x

differentiate 2x^3 + 12x^2 + 12x +5

Using Microsoft Math Solver, you can use your handwriting to input the derivative equation.



Now it is possible to solve your math problem using your hand writing.
Click the image below. Just click the pen icon symbol

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