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Differentiation of Elementary Functions

Fill in the blank:
$\frac{d}{dx}\left[5x\right]=$ __________.

$\frac{5}{1+25x^2}$

$\frac{1}{1-25x^2}$

$1+5x$

Fill in the blank:
$\frac{d}{dx}\left[\cot4x\right]=$ __________.

$x$

$-x$

$-4x$

Fill in the blank:
$\frac{d}{dx}\left[\ln x^2\right]=$ __________.

$\frac{2}{x}$

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

$x^2$

Fill in the blank:
$\frac{d}{dx}\left[e^{5x}\right]=$ __________.

$-e^x$

$e^x\ln\ln a$

$5e^{5x}$

Fill in the blank:
$\frac{d}{dx}\left[\sec\left(2x\right)\right]=$ __________.

$2\sec2x\tan2x$

$\tan2x$

$-\sec2x\tan x$

Fill in the blank:
$\frac{d}{dx}\left[\cos3x\right]=$ __________.

$\tan\left(3x\right)$

$-3\sin\left(3x\right)$

$3\sin\left(x\right)$

Fill in the blank:
$\frac{d}{dx}\left[3x^4\right]=$ __________.

$12x^3$

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

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

Fill in the blank:
$\frac{d}{dx}\left[\sinh3x\right]=$ __________.

$-3\cosh x$

$nx$

$3\cosh3x$

Fill in the blank:
$\frac{d}{dx}\left[\tanh2x\right]=$ __________.

$h2x$

$hx$

$2h2x$

Fill in the blank:
$\frac{d}{dx}\left[a^{2x}\right]=$ __________.

$-a^x$

$2a^{2x}\ln\ln a$

$a^x$

Questions

Time

Score

Differentiation of Elementary Functions

Fill in the blank:﻿ddx[5x]=\frac{d}{dx}\left[5x\right]=dxd​[5x]=﻿ __________.

﻿51+25x2\frac{5}{1+25x^2}1+25x25​﻿

﻿11−25x2\frac{1}{1-25x^2}1−25x21​﻿

﻿1+5x1+5x1+5x﻿

Fill in the blank:﻿ddx[cot⁡4x]=\frac{d}{dx}\left[\cot4x\right]=dxd​[cot4x]=﻿ __________.

﻿xxx﻿

﻿−x-x−x﻿

﻿−4x-4x−4x﻿

Fill in the blank:﻿ddx[ln⁡x2]=\frac{d}{dx}\left[\ln x^2\right]=dxd​[lnx2]=﻿ __________.

﻿2x\frac{2}{x}x2​﻿

﻿1x2\frac{1}{x^2}x21​﻿

﻿x2x^2x2﻿

Fill in the blank:﻿ddx[e5x]=\frac{d}{dx}\left[e^{5x}\right]=dxd​[e5x]=﻿ __________.

﻿−ex-e^x−ex﻿

﻿exln⁡ln⁡ae^x\ln\ln aexlnlna﻿

﻿5e5x5e^{5x}5e5x﻿

Fill in the blank:﻿ddx[sec⁡(2x)]=\frac{d}{dx}\left[\sec\left(2x\right)\right]=dxd​[sec(2x)]=﻿ __________.

﻿2sec⁡2xtan⁡2x2\sec2x\tan2x2sec2xtan2x﻿

﻿tan⁡2x\tan2xtan2x﻿

﻿−sec⁡2xtan⁡x-\sec2x\tan x−sec2xtanx﻿

Fill in the blank:﻿ddx[cos⁡3x]=\frac{d}{dx}\left[\cos3x\right]=dxd​[cos3x]=﻿ __________.

﻿tan⁡(3x)\tan\left(3x\right)tan(3x)﻿

﻿−3sin⁡(3x)-3\sin\left(3x\right)−3sin(3x)﻿

﻿3sin⁡(x)3\sin\left(x\right)3sin(x)﻿

Fill in the blank:﻿ddx[3x4]=\frac{d}{dx}\left[3x^4\right]=dxd​[3x4]=﻿ __________.

﻿12x312x^312x3﻿

﻿11+x2\frac{1}{1+x^2}1+x21​﻿

﻿11−x2\frac{1}{1-x^2}1−x21​﻿

Fill in the blank:﻿ddx[sinh⁡3x]=\frac{d}{dx}\left[\sinh3x\right]=dxd​[sinh3x]=﻿ __________.

﻿−3cosh⁡x-3\cosh x−3coshx﻿

﻿nxnxnx﻿

﻿3cosh⁡3x3\cosh3x3cosh3x﻿

Fill in the blank:﻿ddx[tanh⁡2x]=\frac{d}{dx}\left[\tanh2x\right]=dxd​[tanh2x]=﻿ __________.

﻿h2xh2xh2x﻿

﻿hxhxhx﻿

﻿2h2x2h2x2h2x﻿

Fill in the blank:﻿ddx[a2x]=\frac{d}{dx}\left[a^{2x}\right]=dxd​[a2x]=﻿ __________.

﻿−ax-a^x−ax﻿

﻿2a2xln⁡ln⁡a2a^{2x}\ln\ln a2a2xlnlna﻿

﻿axa^xax﻿

Incorrect

Great!

Fill in the blank:
$\frac{d}{dx}\left[5x\right]=$ __________.

$\frac{5}{1+25x^2}$

$\frac{1}{1-25x^2}$

$1+5x$

Fill in the blank:
$\frac{d}{dx}\left[\cot4x\right]=$ __________.

$x$

$-x$

$-4x$

Fill in the blank:
$\frac{d}{dx}\left[\ln x^2\right]=$ __________.

$\frac{2}{x}$

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

$x^2$

Fill in the blank:
$\frac{d}{dx}\left[e^{5x}\right]=$ __________.

$-e^x$

$e^x\ln\ln a$

$5e^{5x}$

Fill in the blank:
$\frac{d}{dx}\left[\sec\left(2x\right)\right]=$ __________.

$2\sec2x\tan2x$

$\tan2x$

$-\sec2x\tan x$

Fill in the blank:
$\frac{d}{dx}\left[\cos3x\right]=$ __________.

$\tan\left(3x\right)$

$-3\sin\left(3x\right)$

$3\sin\left(x\right)$

Fill in the blank:
$\frac{d}{dx}\left[3x^4\right]=$ __________.

$12x^3$

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

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

Fill in the blank:
$\frac{d}{dx}\left[\sinh3x\right]=$ __________.

$-3\cosh x$

$nx$

$3\cosh3x$

Fill in the blank:
$\frac{d}{dx}\left[\tanh2x\right]=$ __________.

$h2x$

$hx$

$2h2x$

Fill in the blank:
$\frac{d}{dx}\left[a^{2x}\right]=$ __________.

$-a^x$

$2a^{2x}\ln\ln a$

$a^x$