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Differentiation of Trigonometric Functions

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

$2\cos x-\sin x$

$\cos x+\sin x$

$\cos x-\sin x$

Fill in the blank:
$\frac{d}{dx}\left[\frac{\sin x}{1+\cos x}\right]=$ __________.

$\frac{x}{1+\cos x}$

$\frac{\sin x}{1+\cos x}$

$\frac{1}{1+\cos x}$

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

$2\cos x-\sin x$

$\cos x+\sin x$

$x\cos x+\sin x$

Fill in the blank:
$\frac{d}{dx}\left[\frac{\tan x-1}{\sec x}\right]=$ __________.

$\frac{\left[\sec^2x-\tan x\right]}{x^2}$

$\cos x+\sin x$

$\frac{\left[x-\tan x\right]}{x^2}$

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

$2e^x\cos x-\sin x$

$e^x\left[\cos x-\sin x\right]$

$e^x\left[\cos x+\sin x\right]$

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

$2e^x\cos x-\sin x$

$e^x\left[\cos x-\sin x\right]$

$e^x\left[\cos x+\sin x\right]$

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

$x\cos2x+\cos x$

$\cos2x+\sin x\cos x$

$x\cos2x+\sin x\cos x$

Fill in the blank:
$\frac{d}{dx}\left[4\sec t+\tan t\right]=$ __________.

$2\cos t-\sin t$

$\cos t+\sec^2t$

$4\sec\sec t\tan\tan t+\sec^2t$

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

$\frac{\left[\sec^2x-\tan x\right]}{x^2}$

$\frac{\left[x\sec^2x-\tan x\right]}{x^2}$

$\frac{\left[x-\tan x\right]}{x^2}$

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

$-\sin x-2x$

$\cos x+\sin x$

$x\cos x+\sin x$

Questions

Time

Score

Differentiation of Trigonometric Functions

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

﻿2cos⁡x−sin⁡x2\cos x-\sin x2cosx−sinx﻿

﻿cos⁡x+sin⁡x\cos x+\sin xcosx+sinx﻿

﻿cos⁡x−sin⁡x\cos x-\sin xcosx−sinx﻿

Fill in the blank:﻿ddx[sin⁡x1+cos⁡x]=\frac{d}{dx}\left[\frac{\sin x}{1+\cos x}\right]=dxd​[1+cosxsinx​]=﻿ __________.

﻿x1+cos⁡x\frac{x}{1+\cos x}1+cosxx​﻿

﻿sin⁡x1+cos⁡x\frac{\sin x}{1+\cos x}1+cosxsinx​﻿

﻿11+cos⁡x\frac{1}{1+\cos x}1+cosx1​﻿

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

﻿2cos⁡x−sin⁡x2\cos x-\sin x2cosx−sinx﻿

﻿cos⁡x+sin⁡x\cos x+\sin xcosx+sinx﻿

﻿xcos⁡x+sin⁡xx\cos x+\sin xxcosx+sinx﻿

Fill in the blank:﻿ddx[tan⁡x−1sec⁡x]=\frac{d}{dx}\left[\frac{\tan x-1}{\sec x}\right]=dxd​[secxtanx−1​]=﻿ __________.

﻿[sec⁡2x−tan⁡x]x2\frac{\left[\sec^2x-\tan x\right]}{x^2}x2[sec2x−tanx]​﻿

﻿cos⁡x+sin⁡x\cos x+\sin xcosx+sinx﻿

﻿[x−tan⁡x]x2\frac{\left[x-\tan x\right]}{x^2}x2[x−tanx]​﻿

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

﻿2excos⁡x−sin⁡x2e^x\cos x-\sin x2excosx−sinx﻿

﻿ex[cos⁡x−sin⁡x]e^x\left[\cos x-\sin x\right]ex[cosx−sinx]﻿

﻿ex[cos⁡x+sin⁡x]e^x\left[\cos x+\sin x\right]ex[cosx+sinx]﻿

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

﻿2excos⁡x−sin⁡x2e^x\cos x-\sin x2excosx−sinx﻿

﻿ex[cos⁡x−sin⁡x]e^x\left[\cos x-\sin x\right]ex[cosx−sinx]﻿

﻿ex[cos⁡x+sin⁡x]e^x\left[\cos x+\sin x\right]ex[cosx+sinx]﻿

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

﻿xcos⁡2x+cos⁡xx\cos2x+\cos xxcos2x+cosx﻿

﻿cos⁡2x+sin⁡xcos⁡x\cos2x+\sin x\cos xcos2x+sinxcosx﻿

﻿xcos⁡2x+sin⁡xcos⁡xx\cos2x+\sin x\cos xxcos2x+sinxcosx﻿

Fill in the blank:﻿ddx[4sec⁡t+tan⁡t]=\frac{d}{dx}\left[4\sec t+\tan t\right]=dxd​[4sect+tant]=﻿ __________.

﻿2cos⁡t−sin⁡t2\cos t-\sin t2cost−sint﻿

﻿cos⁡t+sec⁡2t\cos t+\sec^2tcost+sec2t﻿

﻿4sec⁡sec⁡ttan⁡tan⁡t+sec⁡2t4\sec\sec t\tan\tan t+\sec^2t4secsecttantant+sec2t﻿

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

﻿[sec⁡2x−tan⁡x]x2\frac{\left[\sec^2x-\tan x\right]}{x^2}x2[sec2x−tanx]​﻿

﻿[xsec⁡2x−tan⁡x]x2\frac{\left[x\sec^2x-\tan x\right]}{x^2}x2[xsec2x−tanx]​﻿

﻿[x−tan⁡x]x2\frac{\left[x-\tan x\right]}{x^2}x2[x−tanx]​﻿

Fill in the blank:﻿ddx[cos⁡x−2tan⁡x]=\frac{d}{dx}\left[\cos x-2\tan x\right]=dxd​[cosx−2tanx]=﻿ __________.

﻿−sin⁡x−2x-\sin x-2x−sinx−2x﻿

﻿cos⁡x+sin⁡x\cos x+\sin xcosx+sinx﻿

﻿xcos⁡x+sin⁡xx\cos x+\sin xxcosx+sinx﻿

Incorrect

Great!

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

$2\cos x-\sin x$

$\cos x+\sin x$

$\cos x-\sin x$

Fill in the blank:
$\frac{d}{dx}\left[\frac{\sin x}{1+\cos x}\right]=$ __________.

$\frac{x}{1+\cos x}$

$\frac{\sin x}{1+\cos x}$

$\frac{1}{1+\cos x}$

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

$2\cos x-\sin x$

$\cos x+\sin x$

$x\cos x+\sin x$

Fill in the blank:
$\frac{d}{dx}\left[\frac{\tan x-1}{\sec x}\right]=$ __________.

$\frac{\left[\sec^2x-\tan x\right]}{x^2}$

$\cos x+\sin x$

$\frac{\left[x-\tan x\right]}{x^2}$

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

$2e^x\cos x-\sin x$

$e^x\left[\cos x-\sin x\right]$

$e^x\left[\cos x+\sin x\right]$

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

$2e^x\cos x-\sin x$

$e^x\left[\cos x-\sin x\right]$

$e^x\left[\cos x+\sin x\right]$

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

$x\cos2x+\cos x$

$\cos2x+\sin x\cos x$

$x\cos2x+\sin x\cos x$

Fill in the blank:
$\frac{d}{dx}\left[4\sec t+\tan t\right]=$ __________.

$2\cos t-\sin t$

$\cos t+\sec^2t$

$4\sec\sec t\tan\tan t+\sec^2t$

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

$\frac{\left[\sec^2x-\tan x\right]}{x^2}$

$\frac{\left[x\sec^2x-\tan x\right]}{x^2}$

$\frac{\left[x-\tan x\right]}{x^2}$

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

$-\sin x-2x$

$\cos x+\sin x$

$x\cos x+\sin x$