Question 1

$\frac{d}{dx}e^u=$

Accepted Answer

$u'e^u$

Answer

$e^u$

Answer

$\frac{u'}{u}$

Answer

$u'a^u$ln$a$

Question 2

$\frac{d}{{dx}}{u^n} = $

Accepted Answer

$n{u^{n - 1}}u'$

Answer

$ - \frac{{u'}}{{1 + {u^2}}}$

Answer

$uv' + vu'$

Answer

$u'{a^u}\ln a$

Question 3

$\frac{d}{{dx}}\left( {uv} \right) = $

Accepted Answer

$uv' + vu'$

Answer

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

Answer

$uv' - vu'$

Answer

$\frac{{vu' - uv'}}{{{v^2}}}$

Question 4

$\frac{d}{{dx}}\left( {\frac{u}{v}} \right) = $

Accepted Answer

$\frac{{vu' - uv'}}{{{v^2}}}$

Answer

$\frac{{uv' - vu'}}{{{v^2}}}$

Answer

$\frac{{vu' + uv'}}{{{v^2}}}$

Answer

$uv' + vu'$

Question 5

$\frac{d}{{dx}}	an u = $

Accepted Answer

$u'{\sec ^2}u$

Answer

$ - u'{\csc ^2}u$

Answer

$u'\sec u	an u$

Answer

$-u'{\sec ^2}u$

Question 6

$\frac{d}{{dx}}\sin u = $

Accepted Answer

$u'\cos u$

Answer

$ - u'\sin u$

Answer

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

Answer

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

Question 7

$\frac{d}{{dx}}\ln u = $

Accepted Answer

$\frac{{u'}}{u}$

Answer

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

Answer

$\frac{{u'}}{{u\ln a}}$

Answer

$u'{a^u}\ln a$

Question 8

$\frac{d}{{dx}}\sqrt u  = $

Accepted Answer

$\frac{{u'}}{{2\sqrt u }}$

Answer

$\frac{{u'}}{{\sqrt u }}$

Answer

$\frac{{1}}{{2\sqrt u }}$

Answer

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

Question 9

$\frac{d}{{dx}}{a^u} = $

Accepted Answer

$u'{a^u}\ln a$

Answer

$\frac{{u'}}{{u\ln a}}$

Answer

$\frac{{u'}}{u}$

Answer

$u'{a^u}$

Question 10

$\frac{d}{{dx}}\csc u = $

Accepted Answer

$ - u'\csc u\cot u$

Answer

$u'\sec u	an u$

Answer

$  u'\csc u\cot u$

Answer

$ - u'{\csc ^2}u$

Question 11

$\frac{d}{{dx}}{\sec ^{ - 1}}u = $

Accepted Answer

$\frac{{u'}}{{\left| u \right|\sqrt {{u^2} - 1} }}$

Answer

$u'{\sec ^2}u$

Answer

$u'\sec u	an u$

Answer

$ - \frac{{u'}}{{\left| u \right|\sqrt {{u^2} - 1} }}$

Question 12

$\frac{d}{{dx}}\sec u = $

Accepted Answer

$u'\sec u	an u$

Answer

$-u'\sec u	an u$

Answer

$u'{\sec ^2}u$

Answer

$ - u'{\csc ^2}u$

Question 13

$\frac{d}{{dx}}{\cos ^{ - 1}}u = $

Accepted Answer

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

Answer

$ - \frac{{u'}}{{\left| u \right|\sqrt {{u^2} - 1} }}$

Answer

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

Answer

$ - \frac{{u'}}{{1 + {u^2}}}$

Question 14

$\frac{d}{{dx}}{\sin ^{ - 1}}u = $

Accepted Answer

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

Answer

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

Answer

$ - \frac{{u'}}{{1 + {u^2}}}$

Answer

$\frac{{u'}}{{\left| u \right|\sqrt {{u^2} - 1} }}$

Question 15

$\frac{d}{{dx}}{	an ^{ - 1}}u = $

Accepted Answer

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

Answer

$ - \frac{{u'}}{{1 + {u^2}}}$

Answer

$u'{\sec ^2}u$

Answer

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

Question 16

$\frac{d}{{dx}}{\log _a}u = $

Accepted Answer

$\frac{{u'}}{{u\ln a}}$

Answer

$u'{a^u}\ln a$

Answer

$-\frac{{u'}}{{u\ln a}}$

Answer

$\frac{{u'}}{u}$

Question 17

$\frac{d}{{dx}}{\csc ^{ - 1}}u = $

Accepted Answer

$ - \frac{{u'}}{{\left| u \right|\sqrt {{u^2} - 1} }}$

Answer

$\frac{{u'}}{{\left| u \right|\sqrt {{u^2} - 1} }}$

Answer

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

Answer

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

Question 18

$\frac{d}{{dx}}\cot u = $

Accepted Answer

$ - u'{\csc ^2}u$

Answer

$ - u'\sin u$

Answer

$ - u'\csc u\cot u$

Answer

$u'{\sec ^2}u$

Question 19

$\frac{d}{{dx}}\cos u = $

Accepted Answer

$ - u'\sin u$

Answer

$u'{\sec ^2}u$

Answer

$u'\sec u	an u$

Answer

$u'\cos u$

Question 20

$\frac{d}{{dx}}{\cot ^{ - 1}}u = $

Accepted Answer

$ - \frac{{u'}}{{1 + {u^2}}}$

Answer

$ - \frac{{u'}}{{\left| u \right|\sqrt {{u^2} - 1} }}$

Answer

$\frac{{vu' - uv'}}{{{v^2}}}$

Answer

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

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