Derivatives

Question 1

Trig Identity 1

Accepted Answer

$sin^2x+cos^2x=1$

Question 2

Trig Identity 2

Accepted Answer

$tan^2x+1=sec^2x$

Question 3

Trig Identity 3

Accepted Answer

$1+cot^2x=csc^2x$

Question 4

Product Rule

Accepted Answer

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

Question 5

Quotient Rule

Accepted Answer

$\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{f'(x)g(x)-g'(x)f(x)}{g(x)^2}$

Question 6

$\frac{d}{dx}(sinx)

Accepted Answer

$cosx$

Question 7

$\frac{d}{dx}(cosx)$

Accepted Answer

$-sinx$

Question 8

$\frac{d}{dx}(tanx)$

Accepted Answer

$sec^2x$

Question 9

$\frac{d}{dx}(cscx)$

Accepted Answer

$-cscxcotx$

Question 10

$\frac{d}{dx}(secx)$

Accepted Answer

$secxtanx$

Question 11

$\frac{d}{dx}(cotx)$

Accepted Answer

$-csc^2x$

Question 12

$sin2x$

Accepted Answer

$2sinxcosx$

Question 13

$cos2x$

Accepted Answer

$cos^2x-sin^2x$ $1-2sin^2x$ $2cos^2x-1$

Question 14

$\frac{d}{dx}[sin^{-1}(x)]$

Accepted Answer

$\frac{x'}{\sqrt{1-x^2}}$

Question 15

$\frac{d}{dx}[cos^{-1}(x)]$

Accepted Answer

$\frac{-x'}{\sqrt{1-x^2}}$

Question 16

$\frac{d}{dx}[tan^{-1}(x)]$

Accepted Answer

$\frac{x'}{1+x^2}$

Question 17

$\frac{d}{dx}[e^x]$

Accepted Answer

$e^x*x'$

Question 18

$\ln{a^x}$

Accepted Answer

$x\ln{a}$

Question 19

$\ln{ab}$

Accepted Answer

$\ln{a}+\ln{b}$

Question 20

$\ln{\frac{a}{b}}$

Accepted Answer

$\ln{a}-\ln{b}$

Question 21

$\ln{e}$

Accepted Answer

$1$

Question 22

$\ln{1}$

Accepted Answer

$0$

Question 23

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

Accepted Answer

$\frac{x'}{x}$

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