Class 12

Differentiation Rules and their Significance

Differentiation is a mathematical technique for determining the derivative of a function involving two independent variables. This procedure is designed to determine the instantaneous changes that occur in one of the variables as a result of the changes that occur in the other variable. For example, the instantaneous change in the rate of displacement when […]

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

Theorems of Derivatives

The algebraic process for calculating derivatives is known as differentiation. The slope or gradient of a particular graph at any given position is the derivative of a function. The tangent’s value drawn to that curve at any given location is the gradient of that curve. The curve’s gradient varies at different positions along the axis

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

The photodiode solar cell and Zener diode

Let’s take a look at the diode, which is the most common two-terminal electronic device. Diodes are two-terminal electrical components that are designed to conduct electricity in just one way. They are small and inexpensive. There are many different types of diodes accessible, including the Light-Emitting Diode (LED), the Laser diode, the Avalanche diode, the

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

Tangents and Normals

Introduction Derivatives play a significant role in mathematics. They refer to the rate of change of functions concerning variables. There is a particular branch of application of derivatives that is concerned with finding the tangents and normals to a given curve.  This branch is of great significance. It helps to find the minima and maxima

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

Tangent equation of tangent and normal

The term “tangent” means “to touch”. The Latin word for the same is “tangere”. In general, we can say that the line that intersects the circle exactly at one point on its circumference and never enters the circle’s interior is a tangent. A circle can have many tangents. They are perpendicular to the radius. Derivatives

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

Tangent

The word tangent means “To touch”. “Tangere” is the Latin term for the same thing. In general, a tangent is a line that meets the circle precisely at one point on its circumference but never enters the circle’s interior. Many tangents can exist in a circle. They run parallel to the radius. In mathematics, derivatives

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

Special Methods of Differentiation Used in Maths

The geometrical meaning of a derivative is the instantaneous rate of change of the function with respect to one of its variables in calculus. The derivative of a function is well characterised by the first principle of derivative. The slope of tangent to the graph at a location is defined by the first derivative of

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

Special Methods of Differentiation

In Calculus, a derivative is the instantaneous rate of change of a function with respect to one of its variables, and in geometry, a derivative is the geometric meaning of a derivative. The derivative of a function is well defined according to the first derivative principle. This is defined as the slope of the graph

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

SCATTER PLOT

In this diagram, dots represent different values of the variables. Scattered plots, which depict the values of variables in a data set by displaying their positions on the vertical and horizontal axes, are characterised by the use of Cartesian coordinates to indicate their positions on the vertical and horizontal axes, respectively. In addition to scatter

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals

Quotient Rule in Differentiation

One way to obtain an expression’s derivative or differentiation in calculus is to take the ratio or division of two differentiable functions and divide it by the expression. By this, I mean that while trying to get the derivative of f(x)/g(x), we can use the rule of quotients, because both of these functions are differentiable

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Applications of Derivatives, Class 12, IIT JEE, Maths, Tangents and normals