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Subscribe to our Newsletter Get the latest tips, news, and developments. Algebra” derives from the first word of the famous text composed by Al-Khwarizmi. The name of this book is Al-Jabr wa’l muqabalah. Al-Khwarizmi also wrote a treatise on Hindu-Arabic numerals. What Is the Greatest Integer Function?
Interactive simulation the most controversial math riddle ever! This course is an introduction to differential calculus. They examine the basic concept of differentiation and practice differentiation techniques. Students develop competence applying differentiation to solve problems. Use derivatives to find extreme values of functions.
Find local extrema using the first derivative of a monotonic function. Use the Mean Value Theorem to find the derivative of a continuous function. Approximate a solution to an equation using Newton’s method. Recover the antiderivative of simple polynomial and trigonometric functions. Determine the effects of operations on a graph. Calculate slopes of tangent lines at given points. Determine the continuity of functions at given points.
Compute the derivatives of linear, quadratic, and polynomial functions. Find the derivative of the sum and difference of two functions. Find the derivative of the ratio and the product of two functions. Recognize derivatives as rates of change. Calculate the derivative of multivariable expressions, implicit differentiation. Derive rates of change from related known rates of change.
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Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice. The graph of a function, drawn in black, and a tangent line to that function, drawn in red. The slope of the tangent line equals the derivative of the function at the marked point. In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.
The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration. Differentiation has applications to nearly all quantitative disciplines. The reaction rate of a chemical reaction is a derivative. Derivatives are frequently used to find the maxima and minima of a function. Equations involving derivatives are called differential equations and are fundamental in describing natural phenomena.
A general function is not a line, so it does not have a slope. A closely related notion is the differential of a function. Treatise on Equations, established conditions for some cubic equations to have solutions, by finding the maxima of appropriate cubic polynomials. The historian of science, Roshdi Rashed, has argued that al-Tūsī must have used the derivative of the cubic to obtain this result.