Editing Derivative (section)

=== Rules for basic functions ===
The following are the rules for the derivatives of the most common basic functions. Here, <math> a </math> is a real number, and <math> e </math> is [[e (mathematical constant)|the base of the natural logarithm, approximately {{nowrap|1=2.71828}}]].<ref>{{harvnb|Varberg|Purcell|Rigdon|2007}}. See p. 133 for the power rule, pp. 115–116 for the trigonometric functions, p. 326 for the natural logarithm, pp. 338–339 for exponential with base {{tmath|1= e }}, p. 343 for the exponential with base {{tmath|1= a }}, p. 344 for the logarithm with base {{tmath|1= a }}, and p. 369 for the inverse of trigonometric functions.</ref> 
* ''[[Power rule|Derivatives of powers]]'':
*: <math> \frac{d}{dx}x^a = ax^{a-1} </math>
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* ''Functions of [[Exponential function|exponential]], [[natural logarithm]], and [[logarithm]] with general base'':
*: <math> \frac{d}{dx}e^x = e^x </math>
*: <math> \frac{d}{dx}a^x = a^x\ln(a)  </math>, for <math> a > 0 </math>
*: <math> \frac{d}{dx}\ln(x) = \frac{1}{x} </math>, for <math> x > 0 </math>
*: <math> \frac{d}{dx}\log_a(x) = \frac{1}{x\ln(a)}  </math>, for <math> x, a > 0 </math>
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* ''[[Trigonometric functions]]'':
*: <math> \frac{d}{dx}\sin(x) = \cos(x) </math>
*: <math> \frac{d}{dx}\cos(x) = -\sin(x) </math>
*: <math> \frac{d}{dx}\tan(x) = \sec^2(x) = \frac{1}{\cos^2(x)} = 1 + \tan^2(x) </math>
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* ''[[Inverse trigonometric functions]]'':
*: <math> \frac{d}{dx}\arcsin(x) = \frac{1}{\sqrt{1-x^2}} </math>, for <math> -1 < x < 1 </math>
*: <math> \frac{d}{dx}\arccos(x)= -\frac{1}{\sqrt{1-x^2}} </math>, for <math> -1 < x < 1 </math>
*: <math> \frac{d}{dx}\arctan(x)= \frac{1}{{1+x^2}} </math>
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