# Calculus

• Derivative of Exponential Functions - The derivative of an exponential function with the base 'a' and exponent 'x' is given by the formula y = d/dx (a^x) = a^x * ln(a). This calculator helps find the derivative.
• First-Order Linear Differential Equations - This calculator helps find the value of the dependent variable in a first-order linear differential equation.
• Gradient of a Function - The gradient of a scalar function comprises its partial derivatives and represents the direction of the steepest ascent. This page explains how to calculate and interpret the gradient.
• Gradient of a Scalar Field - The gradient of a scalar field points in the direction of the greatest rate of increase of the scalar field.
• Calculus - Higher Order Derivatives - Higher order derivatives represent the nth derivative of a function. The second derivative is used to calculate acceleration, while higher orders have other applications in physics and engineering.
• Homogeneous Differential Equations - Homogeneous differential equations are represented as M(x, y)dx + N(x, y)dy = 0 and are solved using techniques like substitution or separation of variables.
• Integration of Hyperbolic Functions - Find the antiderivative of the hyperbolic sine function using this integration calculator.
• Integration of Hyperbolic Sine (sinh) - Learn how to integrate the hyperbolic sine function (sinh) to get the hyperbolic cosine function (cosh) plus a constant. Useful in fields like mathematics and physics.
• Integration of Rational Functions - The integration of rational functions involves finding the antiderivative of a ratio of polynomials. This process may require techniques such as partial fraction decomposition or substitution.
• Laplace's Equation - Laplace's equation is a second-order partial differential equation that describes the behavior of harmonic functions and arises in various areas of physics.
• Calculus - Mean Value Theorem - The Mean Value Theorem describes the relationship between the derivative of a function and its average rate of change over an interval.
• Power Rule for Derivatives - The power rule states that the derivative of a function of the form f(x) = x^n is f'(x) = nx^(n-1). Use this calculator to find the derivative of a polynomial function.
• Second-Order Linear Differential Equations - This calculator evaluates the second-order linear differential equation for the given values of t, a, b, and c.
• Volume of a Solid of Revolution - This formula calculates the volume of a solid of revolution obtained by rotating a circle around its axis.
• Volume of a Solid of Revolution - Disk Method - Learn how to calculate the volume of a solid of revolution using the disk method. Find the formula and explanation for calculating the volumes of solids generated by revolving a region around an axis.