| constant multiple rule | \[\frac{d}{dx}\big(cf\left(x\right)\big) = cf'\left(x\right)\] |
| polynomial rule | \[\frac{d}{dx}\left(x^n\right) = nx^{n-1}\] |
| exponent rules | \[\frac{d}{dx}\left(e^{g(x)}\right) = e^{g(x)}g'(x)\] |
| | \[\frac{d}{dx}\left(c^{g(x)}\right) = c^{g(x)}g'(x)\ln c\] |
| log rule | \[\frac{d}{dx}\big(\log _c g\left(x\right)\big) = \frac{g'(x)}{g(x)\ln c}\] |
| sum rule | \[\frac{d}{dx}\big(f\left(x\right) + g\left(x\right)\big) = f'(x) + g'(x)\] |
| product rule | \[\frac{d}{dx}\big(f\left(x\right)g\left(x\right)\big) = f'(x)g(x) + f(x)g'(x)\] |
| quotient rule | \[\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}\] |
| chain rule | \[\frac{d}{dx}\big(f\left(g\left(x\right)\right)\big) = f'\left(g\left(x\right)\right)g'(x)\] |
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| vector rule | \[x,a \in \mathbb{R}^n: \frac{d}{dx} a^Tx = \frac{d}{dx} x^Ta = a\] |
| matrix rule | \[x\in\mathbb{R}^n, B\in\mathbb{R}^{n\times n} : \frac{d}{dx} x^TBx = (B + B^T) x\]
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Place completed exams on the table by the door in the back of the room.
| product rule | \[\log_a (XY) = \log_a X + \log_a Y\] |
| quotient rule | \[\log_a \left(\frac{X}{Y}\right) = \log_a X - \log_a Y\] |
| power rule | \[\log_a(X^n) = n\log_a X\] |
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Exam Typos
#3: X is number of peers that have the same project as youYou are one of the 75 students in the course.
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