## How to Calculate a Derivative Using Our Derivative Calculator

Our Derivative Calculator is a tool created to simplify the process of differentiating equations. To use it, follow these simple steps:

**Input the Equation**: Enter the mathematical function you wish to differentiate. Make sure it's correctly formatted to avoid errors.**Specify the Variable**: Choose the variable in your equation that you're differentiating with respect to, (this is most often x).**Define the Point (optional)**: If you need the derivative at a specific point, enter its value. This step is optional and can be skipped for a general derivative.**Set the Number of Differentiations**: Decide how many times you want to differentiate the equation.**Calculate**: Click the 'Calculate' button to get your result. The calculator will solve the differentiated equation and, if specified, the derivative value at the chosen point.

## How to Differentiate an Equation Using Derivative Formulas

Differentiating an equation manually requires a solid understanding of derivative formulas. Here's a basic guide:

**Identify the Function Type**: Determine if your function is a polynomial, trigonometric, exponential, or another type.**Apply the Relevant Formula (listed below)**: Use the appropriate derivative formula. For example, the power rule for polynomials or the product rule for products of functions.**Simplify**: After applying the formula, simplify the expression to get the final derivative.

## What is a Derivative in Calculus

A derivative represents the rate at which a function is changing at any given point. In mathematical terms, it's the slope of the tangent line to the function at a specific point. Derivatives are fundamental in calculus and have applications in various fields like physics, engineering, and economics.

## Derivative Formulas List

Here's a list of common derivative formulas:

**Power Rule**: d/dx [x^n] = nx^(n-1)**Product Rule**: d/dx [f(x)g(x)] = f '(x)g(x) + f(x)g'(x)**Quotient Rule**: d/dx [f(x)/g(x)] = (f '(x)g(x) - f(x)g'(x)) / g(x)^2**Chain Rule**: d/dx [f(g(x))] = f '(g(x)) * g'(x)**Trigonometric Functions**:- d/dx [sin(x)] = cos(x)
- d/dx [cos(x)] = -sin(x)
- d/dx [tan(x)] = sec^2(x)

**Exponential Functions**:- d/dx [e^x] = e^x
- d/dx [a^x] = ln(a) * a^x, where a > 0 and does not equal 1

**Logarithmic Functions**:- d/dx [ln(x)] = 1/x
- d/dx [log a(x)] = 1 / (x * ln(a)), where a > 0 and does not equal 1

**Inverse Trigonometric Functions**:- d/dx [arcsin(x)] = 1 / sqrt(1 - x^2)
- d/dx [arccos(x)] = -1 / sqrt(1 - x^2)
- d/dx [arctan(x)] = 1 / (1 + x^2)

**Hyperbolic Functions**:- d/dx [sinh(x)] = cosh(x)
- d/dx [cosh(x)] = sinh(x)
- d/dx [tanh(x)] = sech^2(x)

**Good luck and don't forget to bookmark this derivative calculator when you need to convert an eqation to its differentiated form.**