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Differentiation Formulas : We will begin this section with some basic properties and formulas. We will give the properties & formulas in this section in both "prime" notation & "fraction" notation.
Properties
1) (f ( x) ± g ( x ))′ ) = f ′ ( x ) ± g ′ ( x ) OR d ( f (x ) ± g ( x )) = df/dx ± dg/ dx
In other terms, to differentiate a sum or difference all we have to do is differentiate the individual terms & then put them back together with the suitable signs. Note that this property is not limited to two functions.
2) (cf ( x ))′ = cf ′ ( x ) OR d (cf ( x ))/dx = c df/dx , c is any number
In other terms, we can "factor" a multiplicative constant out of derivative if we have to.
Note as well that we have not involved formulas for the derivative of products or quotients of two functions here. The derivative of product or quotient of two of functions is not the product or quotient of the derivatives of individual pieces
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
Here we look at only the rules without going into their proofs. They are: a 0. If a If a If a
Find out the area of the region bounded by y = 2 x 2 + 10 and y = 4 x + 16 . Solution In this case the intersection points (that we'll required eventually) are not going t
It refers to the ratio of the explained variation to the total variation and is utilized to measure the strength of the linear relationship. The stronger the linear relationship th
Area between Two Curves We'll start with the formula for finding the area among y = f(x) and y = g(x) on the interval [a,b]. We will also suppose that f(x) ≥ g(x) on [a,b].
why arcsin(sinq)=pi-q [pi/2 3pi/2]
functions f&g on R to R such that f=\g but fog=gof
Calculate the area and circumference of a circle: Calculate the area and circumference of a circle with a 3" radius. Solution: A = πr2
-cot^2 90^0 + 4 sin 270^0 - 3 tan 180^0
127.78*45
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