If y=e^(mcos-1x), Show: (1 - x^2)y2 - xy1 = m^2y I I Higher Order Derivatives I CBSE I ICSE

If y=e^(mcos-1x), Show: (1 - x^2)y2 - xy1 = m^2y I I Higher Order Derivatives I CBSE I ICSE

Differentiation is a process of finding a function that outputs the rate of change of one variable with respect to another variable
the act or process of differentiating, or the state of being differentiated.
Mathematics. the operation of finding the differential or derivative of a function.
The essence of calculus is the derivative. The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point. Let's use the view of derivatives as tangents to motivate a geometric definition of the derivative.
We want to find the slope of the tangent line to a graph at the point P. We can approximate the slope by drawing a line through the point P and another point nearby, and then finding the slope of that line, called a secant line. The slope of a line is determined using the following formula (m represents slope) :
Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.
The other basic rule, called the chain rule, provides a way to differentiate a composite function. If f(x) and g(x) are two functions, the composite function f(g(x)) is calculated for a value of x by first evaluating g(x) and then evaluating the function f at this value of g(x); for instance, if f(x) = sin x and g(x) = x2, then f(g(x)) = sin x2, while g(f(x)) = (sin x)2. The chain rule states that the derivative of a composite function is given by a product, as D(f(g(x))) = Df(g(x)) ∙ Dg(x). In words, the first factor on the right, Df(g(x)), indicates that the derivative of Df(x) is first found as usual, and then x, wherever it occurs, is replaced by the function g(x)
learning needs, and levels of academic achievement are grouped together. In heterogeneously grouped classrooms, for example, teachers vary instructional strategies and use more flexibly designed lessons to engage student interests and address distinct learning needs—all of which may vary from student to student. The basic idea is that the primary educational objectives—making sure all students master essential knowledge, concepts, and skills—remain the same for every student, but teachers may use different instructional methods to help students meet those expectations.
Teachers who employ differentiated instructional strategies will usually adjust the elements of a lesson from one group of students to another, so that those who may need more time or a different teaching approach to grasp a concept get the specialized assistance they need, while those students who have already mastered a concept can be assigned a different learning activity or move on to a new concept or lesson. In more diverse classrooms, teachers will tailor lessons to address the unique needs of special-education students, high-achieving students, and English-language learners, for example. Teachers also use strategies such as formative assessment—periodic, in-process evaluations of what students are learning or not learning—to determine the best instructional approaches or modifications needed for each student.
Also called “differentiated instruction,” differentiation typically entails modifications to practice (how teachers deliver instruction to students), process (how the lesson is designed for students), products (the kinds of work products students will be asked to complete), content (the specific readings, research, or materials students will study), assessment (how teachers measure what students have learned), and grouping (how students are arranged in the classroom or paired up with other students). Differentiation techniques may also be based on specific student attributes, including interest (what subjects inspire students to learn), readiness (what students have learned and still need to learn), or learning style.

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