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Derivative Calculator
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What is a Derivative Calculator?
This calculator finds derivatives of functions step-by-step, showing the rate of change and slope at any point. Essential for calculus, physics, and engineering.
This calculator finds derivatives of functions step-by-step, showing the rate of change and slope at any point. Essential for calculus, physics, and engineering.
How to Use Derivatives in Math & Science
- Find Slopes: Calculate the slope of tangent lines to curves at specific points.
- Optimization: Find maximum and minimum values by setting derivatives equal to zero.
- Physics Applications: Velocity is the derivative of position, acceleration is the derivative of velocity.
- Rate of Change: Understand how quickly variables change in economics, biology, and engineering.
- Chain Rule: Handle composite functions by applying the chain rule for complex derivatives.
Example: For f(x) = x², the derivative f'(x) = 2x, meaning at x = 3, the slope is 6.
Derivative Result
Enter a function and click "Calculate" to see the derivative result here.
Step-by-Step Solution
Related Math Calculators
How to Use the Derivative Calculator
- Enter your function using standard notation: x^2, sin(x), ln(x), e^x, etc.
- Select the order of derivative (1st, 2nd, 3rd, etc.) from the dropdown.
- Optionally enter a point to evaluate the derivative at that specific x-value.
- Click "Calculate" to see the derivative and step-by-step solution.
Understanding Derivatives
- First Derivative: Gives the slope and rate of change at any point
- Second Derivative: Shows concavity and acceleration
- Higher Derivatives: Provide insight into the function's behavior
Derivative Rules
- Power Rule: d/dx[x^n] = n·x^(n-1)
- Product Rule: d/dx[f·g] = f'·g + f·g'
- Quotient Rule: d/dx[f/g] = (f'·g - f·g')/g²
- Chain Rule: d/dx[f(g(x))] = f'(g(x))·g'(x)
Frequently Asked Questions about Derivative Calculators
This calculator can find derivatives of polynomial, trigonometric, exponential, logarithmic, rational, and composite functions using various differentiation rules.
Enter functions using standard mathematical notation: x^2 for x squared, sin(x) for sine, ln(x) for natural log, e^x for exponential, etc.
Yes, you can calculate first, second, third, and higher-order derivatives by specifying the order of differentiation.