Evaluate The Following Derivatives on Your Calculator

This guide explains how to evaluate derivatives using your calculator, including basic differentiation rules, power rule, product rule, quotient rule, and chain rule. We'll show you step-by-step examples and provide a calculator to practice.

How to Use This Calculator

To evaluate derivatives on your calculator, follow these steps:

Enter the function you want to differentiate in the input field.
Select the variable with respect to which you want to differentiate (usually x).
Click "Calculate" to see the derivative.
Review the result and the step-by-step explanation.

The calculator will show you the derivative of the function you entered, along with a breakdown of how it was calculated.

Derivative Formulas

Here are the basic differentiation rules used in this calculator:

Power Rule

If f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹

Product Rule

If f(x) = u(x)·v(x), then f'(x) = u'(x)·v(x) + u(x)·v'(x)

Quotient Rule

If f(x) = u(x)/v(x), then f'(x) = [u'(x)·v(x) - u(x)·v'(x)] / [v(x)]²

Chain Rule

If f(x) = g(h(x)), then f'(x) = g'(h(x))·h'(x)

The calculator applies these rules automatically when you enter a function. For more complex functions, it may combine these rules as needed.

Worked Examples

Example 1: Power Rule

Find the derivative of f(x) = 3x⁴

Solution: f'(x) = 4·3x³ = 12x³

Example 2: Product Rule

Find the derivative of f(x) = x·eˣ

Solution: f'(x) = eˣ·x + x·eˣ = eˣ(x + 1)

Example 3: Chain Rule

Find the derivative of f(x) = sin(2x)

Solution: f'(x) = cos(2x)·2 = 2cos(2x)

These examples demonstrate how the calculator applies different differentiation rules to find derivatives. You can try similar functions in the calculator to practice.

Frequently Asked Questions

What types of functions can I differentiate with this calculator?

This calculator can differentiate polynomial functions, exponential functions, trigonometric functions, logarithmic functions, and combinations of these using the power, product, quotient, and chain rules.

How do I enter a function with multiple terms?

Enter the function using standard mathematical notation. For example, enter "3x² + 2x - 5" for the function 3x² + 2x - 5. The calculator will differentiate each term separately.

What if my calculator doesn't have a derivative function?

If your calculator doesn't have a built-in derivative function, you can use numerical differentiation methods or graph the function to estimate the derivative. This calculator provides an alternative way to find exact derivatives.

Can I differentiate functions with multiple variables?

This calculator currently supports differentiation with respect to a single variable. For functions with multiple variables, you would need to use partial derivatives.