\frac{dy}{dx} = a \cdot n \cdot x^{n-1}

**First and Second Derivatives:** Get the rate of change and concavity for any function you enter.

**Turning Points:** Automatically calculate and classify turning points (local minima, maxima, or saddle points) using Newton-Raphson methods.

**Points of Inflection**: Find inflection points where the function changes concavity, by solving \( f''(x) = 0 \).

**Generate Interactive Graphs**: The graph shows the original function, its derivatives, and highlights key points (turning points and points of inflection) for a better understanding of the function’s behavior.

Enter the following types of expressions into the input box

**Polynomial Functions:**

Example: x^2

Example: x^3 - 6*x^2 + 9*x + 2

**Trigonometric Functions:**

Example: sin(x)

Example: cos(x)

Example: tan(x)

**Exponential Functions:**

Example: e^x

Example: a^x (replace a with any constant, e.g., 2^x)

**Logarithmic Functions:**

Example: log(x)

Rational Functions:

Example: 1/x

**Square Roots and Radicals:**

Example: sqrt(x)

**Combination of Functions:**

Example: x^2 * sin(x) + e^x

CalculusPop differentiation solver helps you analyze any function through differentiation, providing insights into its behavior with:

First Derivative: Understand the rate of change of your function.

Second Derivative: Explore concavity and acceleration.

Turning Points: Identify local minima, maxima, and saddle points.

Points of Inflection: Locate where the function changes concavity.

Enter Your Function:

In the input box, type your function using standard mathematical notation. Check the examples below to see the correct formats for different types of functions.

Click "Solve":

The solver will compute and display the first and second derivatives. It will also find turning points and points of inflection, along with an interactive graph of the function and its derivatives.

Review the Steps: A detailed step-by-step explanation of the differentiation process is provided so you can understand each phase of the calculation.

The graph shows the original function, its derivatives, and highlights key points (turning points and points of inflection) for a better understanding of the function’s behavior.