![]() ![]() Find the nth derivative of y = cos h2 3x Solution: Write cos h2 3x =įind the nth derivative of : (1) sin h 2x sin 4x Solution: Dn (2) y = log (4x2 – 1) Solution: Let y = log (4x2 – 1) = log Therefore y = log (2x + 1) + log (2x – 1). Y1 = eax Note: sin (A + B) = sin A cos B + cos A sin B y1 = r eax sin ( + bx + c) Similarly we get, y2 = r2 eax sin (2 + bx + c), 圓 = r3 eax sin (3 + bx + c) yn = rn eax sin (n + bx + c)Įxercise: If y = eax cos (bx + c), yn = rn eax cos (n + bx + c), Examples: 1. b cos (bx + c) + aeax sin (bx + c), = eax Put a = r cos , b = r sin Then = tan-1 (b/a) and a2 + b2 = r2 (cos2 + sin2 ) = r2 y = (ax + b)m, where m is a positive integer such that m > n. ![]() (m amx log a) = (m log a)2 amx 圓 = (m log a)3 amx yn = (m log a)n amx.ģ. Nth order derivatives of some standard functions: 1. These two processes act inversely to each other, a fact delivered conclusively by the Fundamental theorem of calculus. The second is the integral calculus ( Part B ), which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. More precisely, the local behavior of functions which can be illustrated by the slope of a function's graph. The first is the differential calculus ( Part A ), which is concerned with the instantaneous rate of change of quantities with respect to other quantities. It is built on two major complementary ideas, both of which rely critically on the concept of limits. ANONYMUS Calculus is a central branch of Mathematics, developed from algebra and geometry. Our product offerings include millions of PowerPoint templates, diagrams, animated 3D characters and more.Differential Calculus To err is human, to admit superhuman, to forgive divine, to blame it on others politics, to repeat unprofessional. is brought to you by CrystalGraphics, the award-winning developer and market-leading publisher of rich-media enhancement products for presentations. Then you can share it with your target audience as well as ’s millions of monthly visitors. We’ll convert it to an HTML5 slideshow that includes all the media types you’ve already added: audio, video, music, pictures, animations and transition effects. ![]() You might even have a presentation you’d like to share with others. And, best of all, it is completely free and easy to use. Whatever your area of interest, here you’ll be able to find and view presentations you’ll love and possibly download. It has millions of presentations already uploaded and available with 1,000s more being uploaded by its users every day. is a leading presentation sharing website. Tangent plane and the line normal to the surfaceįind the equations of the tangent plane and theġ0.9 Cylindrical and spherical polar coordinates Possible rate of change with distance and inĮx Find the expression for the equations of the ![]() Point (1,2-1), find its rate of change with Evaluate the arc length along theġ0.4 Vector functions of several argumentsĮx Find the element of area on the surface of a Differentiation of composite vector expressionsĮx A curve lying in the xy-plane is given by.For two-dimensional plane polar coordinates ![]()
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