By Elliott Mendelson, Frank Ayres

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**Extra info for Calculus Crash Course (Schaum's Easy Outlines Series)**

**Sample text**

Then dy/dx = 2(x - 5). Second method: Differentiate to find Schaum’s Easy Outlines Calculus Page 23 Then, by Rule 12, The Chain Rule For two functions f and g, the function given by the formula f(g(x)) is called a composite function. If f and g are differentiable, then so is the composite function, and its derivative may be obtained by either of two procedures. The first is to compute an explicit formula for f(g(x)) and differentiate. 7 If f(x) = x 2 + 3 and g(x) = 2x + 1, then The derivative of a composite function may also be obtained with the following role: Rule 13.

An arc of a curve y = f(x) is called concave downward if, at each of its points, the arc lies below the tangent at that point. As x increases, f’(x) either is of the same sign and decreasing (as on the interval s < x < c of Figure 3-3) or changes sign from positive to negative (as on the interval a < x < b). In either case, the slope f’(x) is decreasing and f"(x) < 0. Point of Inflection A point of inflection is a point at which a curve changes from concave upward to concave downward, or vice versa.

10 Differentiate y = (x 2 + 4) 2 (2x 3 - 1) 3 . Schaum’s Easy Outlines Calculus Page 25 Higher Derivatives Let y = f(x) be a differentiable function of x, and let its derivative be called the first derivative of the function. If the first derivative is differentiable, its derivative is called the second derivative of the (original) function and is denoted by one of the symbols In turn, the derivative of the second derivative is called the third derivative of the function and is denoted by one of the symbols and so on.