calc exam 2 formulas

Question 1

linear approximation

Accepted Answer

$l(x) = f(a)+f'(a)(x-a)

Question 2

$\frac{d}{dx} (e^{g(x)})

Accepted Answer

$e^{g(x)}	imes{g'(x)}

Question 3

$\frac{d}{dx} (\ln {g(x)})

Accepted Answer

$\frac{1}{g(x)}	imes g'(x)

Question 4

$\frac{d}{dx}(b^{g(x)})

Accepted Answer

$b^{g(x)}	imes g'(x) 	imes \ln b

Question 5

$\frac{d}{dx}(log_bg(x))

Accepted Answer

$\frac{g'(x)}{g(x)lnb}

Question 6

If f''(x) > positive over interval I

Accepted Answer

f is concave up over I

Question 7

If f''(x) is negative over interval I

Accepted Answer

f is concave down over I

Question 8

If f'(c)=0 and f''(c) is positive then

Accepted Answer

f has a local minimum at c

Question 9

If f'(c)=0 and f''(c) is negative then

Accepted Answer

f has a local maximum at c

Question 10

If f'(c)=0 and f''(c)=0 then

Accepted Answer

evaluate at f'(x)

Question 11

chain rule

Accepted Answer

$\frac{d}{dx} f(g(x)) = f'(g(x))g'(x)

Question 12

ln e

Accepted Answer

1

Question 13

$\ln e^x$

Accepted Answer

x

Question 14

ln(xy)

Accepted Answer

ln(x)+ln(y)

Question 15

$\ln(\frac{x}{y})$

Accepted Answer

ln x - ln y

Question 16

$\frac{d}{dx} log_bx$

Accepted Answer

$\frac{1}{x\ln b}$

Question 17

$\frac{d}{dx} \sin x

Accepted Answer

cos x

Question 18

$\frac{d}{dx} 	an x

Accepted Answer

$\sec ^2 x$

Question 19

$\frac{d}{dx}sec x

Accepted Answer

sec x tan x

Question 20

$\frac{d}{dx} \cos x

Accepted Answer

-sin x

Question 21

$\frac{d}{dx} \cot x

Accepted Answer

$-\csc ^2 x

Question 22

$\frac{d}{dx} csc x

Accepted Answer

$-\csc x cot x

Alle Karten