The derivative of the tangent function (tan(x)) is the secant squared function (sec^2(x)). In mathematical notation, it can be represented as: d/dx(tan(x)) = sec^2(x) This means that if you have a function y = tan(x), the rate at which y changes with respect to x (its derivative) is given by sec^2(x). In simpler terms, when … Read more

he derivative of the cosine function (cos(x)) is the negative sine function (-sin(x)). In mathematical notation, it can be represented as: d/dx(cos(x)) = -sin(x) This means that if you have a function y = cos(x), the rate at which y changes with respect to x (its derivative) is given by -sin(x). In simpler terms, when … Read more

The derivative of the sine function (sin(x)) is the cosine function (cos(x)). In mathematical notation, it can be represented as: d/dx(sin(x)) = cos(x) This means that if you have a function y = sin(x), the rate at which y changes with respect to x (its derivative) is given by cos(x). In simpler terms, when you … Read more

The derivatives of trigonometric functions are as follows: These formulas represent the derivatives of the basic trigonometric functions with respect to x. They are widely used in calculus and mathematical analysis to find rates of change, slopes, and other related quantities in trigonometric equations and problems. Here are examples demonstrating the application of the derivatives … Read more

I’ll explain the derivative of arctan(2x) in a simpler way. Imagine you have a big playground, and there are two friends, let’s call them x and y. They are playing a game where x moves along the horizontal line, and y moves along the vertical line. They have a special rule: y’s movement is determined … Read more

The derivative of the arcsin function (also denoted as sin^(-1)(x) or asin(x)) can be found using differentiation techniques. Let’s denote y = arcsin(x), where -1 ≤ x ≤ 1. To find the derivative dy/dx, we can differentiate both sides of the equation y = arcsin(x) with respect to x. Using the chain rule, we have: … Read more

To find the derivative of a fraction, you can use the quotient rule. The quotient rule states that if you have a function of the form f(x) = g(x) / h(x), where both g(x) and h(x) are functions, then the derivative of f(x) with respect to x is given by: f'(x) = (g'(x) * h(x) … Read more