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Differentiation formulas

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

x

-x

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

$-e^x$

$e^x\ln\ln a$

$e^x$

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

hx

-hx

3hx

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

$-a^x$

$a^x\ln\ln a$

$a^x$

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

tanx

-sinx

sinx

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

$\sec x\tan x$

$\tan x$

$-\sec\tan x$

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

$\frac{1}{x}$

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

$x^2$

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

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

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

$1+x$

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

$-\cosh x$

$nx$

$\cosh x$

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

$4x^3$

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

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

Questions

Time

Score

Differentiation formulas

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

x

-x

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

﻿−ex-e^x−ex﻿

﻿exln⁡ln⁡ae^x\ln\ln aexlnlna﻿

﻿exe^xex﻿

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

hx

-hx

3hx

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

﻿−ax-a^x−ax﻿

﻿axln⁡ln⁡aa^x\ln\ln aaxlnlna﻿

﻿axa^xax﻿

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

tanx

-sinx

sinx

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

﻿sec⁡xtan⁡x\sec x\tan xsecxtanx﻿

﻿tan⁡x\tan xtanx﻿

﻿−sec⁡tan⁡x-\sec\tan x−sectanx﻿

Fill in the blank:﻿ddx[ln⁡x]=\frac{d}{dx}\left[\ln x\right]=dxd​[lnx]=﻿

﻿1x\frac{1}{x}x1​﻿

﻿1x2\frac{1}{x^2}x21​﻿

﻿x2x^2x2﻿

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

﻿11+x2\frac{1}{1+x^2}1+x21​﻿

﻿11−x2\frac{1}{1-x^2}1−x21​﻿

﻿1+x1+x1+x﻿

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

﻿−cosh⁡x-\cosh x−coshx﻿

﻿nxnxnx﻿

﻿cosh⁡x\cosh xcoshx﻿

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

﻿4x34x^34x3﻿

﻿11+x2\frac{1}{1+x^2}1+x21​﻿

﻿11−x2\frac{1}{1-x^2}1−x21​﻿

Incorrect

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

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

$-e^x$

$e^x\ln\ln a$

$e^x$

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

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

$-a^x$

$a^x\ln\ln a$

$a^x$

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

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

$\sec x\tan x$

$\tan x$

$-\sec\tan x$

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

$\frac{1}{x}$

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

$x^2$

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

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

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

$1+x$

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

$-\cosh x$

$nx$

$\cosh x$

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

$4x^3$

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

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