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.