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25 Σεπ 2018 · Common Derivatives and Integrals - Here is a set of common derivatives and integrals that are used somewhat regularly in a Calculus I or Calculus II class. Also included are reminders on several integration techniques. Currently this cheat sheet is 4 pages long.
In this booklet we will use both these notations. We can use these results and the rules that we have learnt already to differentiate functions which involve exponentials or logarithms. e (x2 + 3x + 1). We solve this by using the chain rule and our knowledge of the derivative of log x. d = e3x2 (3x2) × dx = 6xe3x2.
ACADEMY MATH CHEAT SHEET Rules of Exponents For any nonzero x, x0 = 1. For any integers p and q, x p q = q √ xp = (q x)p. If p is positive this is defined for all x when q is odd and for nonnegative x when q is even. If p/q is negative, the power x p q is never defined for x = 0. Other exponent rules include xr+s = xrxs (xr)s = xrs (xy)r ...
Chain rule \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx} Common Derivatives \frac{d}{dx}\left(\ln(x))=\frac{1}{x} \frac{d}{dx}\left(\ln(\left|x\right|))=\frac{1}{x}
To differentiate 2 , multiply the whole function by . The derivate is 2 . can be used to model situations such as population growth, where the rate of increase is proportional to the size of the population at any given moment.
We use quotient rule when we have division of one of the 6 differentiation types (easy power, harder power, ln, exponential, trig, inverse trig) (here we have a constant and a harder power type and a constant is not
The derivative of logarithmic function of any base can be obtained converting log a to ln as y = log a x = lnx lna = lnx 1 lna and using the formula for derivative of lnx: So we have d dx log a x = 1 x 1 lna = 1 xlna: The derivative of lnx is 1 x and the derivative of log a x is 1 xlna: To summarize, y ex ax lnx log a x y0 ex ax lna 1 x 1 xlna
