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Questions

1 / 10

Time

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Product Rule

Calculate $\frac{d}{dx}\left[\cos\left(x\right)\ln\left(x\right)\right]$ .

$\sin2x$

$-\sin x\ln x-\frac{\cos x}{x}$

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

Calculate $\frac{d}{dx}\left[4x^2\ln\ln x\right]$ .

$8x\ln x+4x$

$2x\ln x+2$

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

Calculate $\frac{d}{dx}\left[\left(x+5\right)\left(7x\right)\right]$ .

$2+3x$

$-6x+3$

$14x+35$

Calculate $\frac{d}{dx}\left[\left(x+5\right)e^x\right]$ .

$2e^x$

$-6e^x$

$e^x+\left(x+5\right)e^x$

Calculate $\frac{d}{dx}\left[\left(x^2\right)\ln\left(x\right)\right]$ .

$2x\ln x+x$

$2x+2\ln x$

$2x+\ln x$

Calculate $\frac{d}{dx}\left[\left(x^2\right)\left(4\right)\right]$ .

$2x$

$2x+2$

$8x$

Calculate $\frac{d}{dx}\left[\cos\left(x\right)e^x\right]$ .

$\cos x+e^x$

$-\sin xe^x+\cos xe^x$

$-\cos x$

Calculate $\frac{d}{dx}\left[\left(x+1\right)\left(3x\right)\right]$ .

$2x$

$6x+3$

$6x+2$

Calculate $\frac{d}{dx}\left[\cos\left(x\right)\ln\left(x\right)\right]$ .

$\sin2x$

$-\sin x.\ln x+\frac{1}{x}\cos x$

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

Calculate $\frac{d}{dx}\left[\sin\left(x\right)e^x\right]$ .

$\cos xe^x+\sin xe^x$

$\cos xe^x-e^x$

$\cos x-\cos xe^x$

Questions

Time

Score

Product Rule

Calculate ﻿ddx[cos⁡(x)ln⁡(x)]\frac{d}{dx}\left[\cos\left(x\right)\ln\left(x\right)\right]dxd​[cos(x)ln(x)]﻿.

﻿sin⁡2x\sin2xsin2x﻿

﻿−sin⁡xln⁡x−cos⁡xx-\sin x\ln x-\frac{\cos x}{x}−sinxlnx−xcosx​﻿

﻿−sin⁡x+1x-\sin x+\frac{1}{x}−sinx+x1​﻿

Calculate ﻿ddx[4x2ln⁡ln⁡x]\frac{d}{dx}\left[4x^2\ln\ln x\right]dxd​[4x2lnlnx]﻿.

﻿8xln⁡x+4x8x\ln x+4x8xlnx+4x﻿

﻿2xln⁡x+22x\ln x+22xlnx+2﻿

﻿2x−1x2x-\frac{1}{x}2x−x1​﻿

Calculate ﻿ddx[(x+5)(7x)]\frac{d}{dx}\left[\left(x+5\right)\left(7x\right)\right]dxd​[(x+5)(7x)]﻿.

﻿2+3x2+3x2+3x﻿

﻿−6x+3-6x+3−6x+3﻿

﻿14x+3514x+3514x+35﻿

Calculate ﻿ddx[(x+5)ex]\frac{d}{dx}\left[\left(x+5\right)e^x\right]dxd​[(x+5)ex]﻿.

﻿2ex2e^x2ex﻿

﻿−6ex-6e^x−6ex﻿

﻿ex+(x+5)exe^x+\left(x+5\right)e^xex+(x+5)ex﻿

Calculate ﻿ddx[(x2)ln⁡(x)]\frac{d}{dx}\left[\left(x^2\right)\ln\left(x\right)\right]dxd​[(x2)ln(x)]﻿.

﻿2xln⁡x+x2x\ln x+x2xlnx+x﻿

﻿2x+2ln⁡x2x+2\ln x2x+2lnx﻿

﻿2x+ln⁡x2x+\ln x2x+lnx﻿

Calculate ﻿ddx[(x2)(4)]\frac{d}{dx}\left[\left(x^2\right)\left(4\right)\right]dxd​[(x2)(4)]﻿.

﻿2x2x2x﻿

﻿2x+22x+22x+2﻿

﻿8x8x8x﻿

Calculate ﻿ddx[cos⁡(x)ex]\frac{d}{dx}\left[\cos\left(x\right)e^x\right]dxd​[cos(x)ex]﻿.

﻿cos⁡x+ex\cos x+e^xcosx+ex﻿

﻿−sin⁡xex+cos⁡xex-\sin xe^x+\cos xe^x−sinxex+cosxex﻿

﻿−cos⁡x-\cos x−cosx﻿

Calculate ﻿ddx[(x+1)(3x)]\frac{d}{dx}\left[\left(x+1\right)\left(3x\right)\right]dxd​[(x+1)(3x)]﻿.

﻿2x2x2x﻿

﻿6x+36x+36x+3﻿

﻿6x+26x+26x+2﻿

Calculate ﻿ddx[cos⁡(x)ln⁡(x)]\frac{d}{dx}\left[\cos\left(x\right)\ln\left(x\right)\right]dxd​[cos(x)ln(x)]﻿.

﻿sin⁡2x\sin2xsin2x﻿

﻿−sin⁡x.ln⁡x+1xcos⁡x-\sin x.\ln x+\frac{1}{x}\cos x−sinx.lnx+x1​cosx﻿

﻿−sin⁡x+1x-\sin x+\frac{1}{x}−sinx+x1​﻿

Calculate ﻿ddx[sin⁡(x)ex]\frac{d}{dx}\left[\sin\left(x\right)e^x\right]dxd​[sin(x)ex]﻿.

﻿cos⁡xex+sin⁡xex\cos xe^x+\sin xe^xcosxex+sinxex﻿

﻿cos⁡xex−ex\cos xe^x-e^xcosxex−ex﻿

﻿cos⁡x−cos⁡xex\cos x-\cos xe^xcosx−cosxex﻿

Incorrect

Great!

Calculate $\frac{d}{dx}\left[\cos\left(x\right)\ln\left(x\right)\right]$ .

$\sin2x$

$-\sin x\ln x-\frac{\cos x}{x}$

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

Calculate $\frac{d}{dx}\left[4x^2\ln\ln x\right]$ .

$8x\ln x+4x$

$2x\ln x+2$

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

Calculate $\frac{d}{dx}\left[\left(x+5\right)\left(7x\right)\right]$ .

$2+3x$

$-6x+3$

$14x+35$

Calculate $\frac{d}{dx}\left[\left(x+5\right)e^x\right]$ .

$2e^x$

$-6e^x$

$e^x+\left(x+5\right)e^x$

Calculate $\frac{d}{dx}\left[\left(x^2\right)\ln\left(x\right)\right]$ .

$2x\ln x+x$

$2x+2\ln x$

$2x+\ln x$

Calculate $\frac{d}{dx}\left[\left(x^2\right)\left(4\right)\right]$ .

$2x$

$2x+2$

$8x$

Calculate $\frac{d}{dx}\left[\cos\left(x\right)e^x\right]$ .

$\cos x+e^x$

$-\sin xe^x+\cos xe^x$

$-\cos x$

Calculate $\frac{d}{dx}\left[\left(x+1\right)\left(3x\right)\right]$ .

$2x$

$6x+3$

$6x+2$

Calculate $\frac{d}{dx}\left[\cos\left(x\right)\ln\left(x\right)\right]$ .

$\sin2x$

$-\sin x.\ln x+\frac{1}{x}\cos x$

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

Calculate $\frac{d}{dx}\left[\sin\left(x\right)e^x\right]$ .

$\cos xe^x+\sin xe^x$

$\cos xe^x-e^x$

$\cos x-\cos xe^x$