|BSM

Questions

1 / 10

Time

Score

Chain Rule

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sin\sin\left(e^{x^3}\right)$ .

$\cos x^2e^{x^3}\cos\left(e^{x^3}\right)$

$\cos3x^2e^{x^3}\cos\left(e^{x^3}\right)$

$-\left(4x-6\right)$

If $y=f\left(u\right)$ and $u=g\left(x\right)$ . Calculate $\frac{dy}{dx}$ .

$\frac{dy}{du}$

$\frac{dy}{dx}\frac{dx}{du}$

$\frac{dy}{du}\frac{du}{dx}$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sqrt{\tan\left(1+x^2\right)}$ .

$\frac{\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(1+x^2\right)}}$

$\frac{x\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(1+x^2\right)}}$

$\frac{x\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(x^2\right)}}$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\tan\tan\left(x^2\right)$ .

$2x\sec\left(x^2\right)$

$2\sec\left(x^2\right)$

$2x\sec^2\left(x^2\right)$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sin\sin\left(e^{x^2}\right)$ .

$\cos x^2e^{x^3}\cos\left(e^{x^3}\right)$

$\cos3x^2e^{x^2}\cos\left(e^{x^2}\right)$

$\cos2xe^{x^2}\cos\left(e^{x^2}\right)$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\cos\cos\left(\tan x\right)$ .

$2x\cos\left(x^2\right)$

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

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

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sin\sin\left(x^2\right)$ .

$2x\cos\left(x^2\right)$

$2\cos\left(x^2\right)$

$x\cos\left(x^2\right)$

Use chain rule to find $\frac{dy}{dx}$ , if $y=f\left(u\right)=u+1$ and $x=u+\frac{1}{u}$ .

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

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

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

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sin\sin\left(2x^2-6x\right)$ .

$\left(4x-6\right)\cos\cos\left(2x^2-6x\right)$

$\cos\cos\left(2x^2-6x\right)$

$-\left(4x-6\right)$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sqrt{x+\sqrt{x}}$ .

$\frac{2\sqrt{x}}{4\sqrt{x+\sqrt{x}}\sqrt{x}}$

$\frac{2\sqrt{x}+1}{4\sqrt{x+\sqrt{x}}\sqrt{x}}$

$\frac{\sqrt{x}+1}{4\sqrt{x+\sqrt{x}}\sqrt{x}}$

Questions

Time

Score

Chain Rule

Use chain rule to find ﻿f′(x)f'\left(x\right)f′(x)﻿, if ﻿f(x)=sin⁡sin⁡(ex3)f\left(x\right)=\sin\sin\left(e^{x^3}\right)f(x)=sinsin(ex3)﻿.

﻿cos⁡x2ex3cos⁡(ex3)\cos x^2e^{x^3}\cos\left(e^{x^3}\right)cosx2ex3cos(ex3)﻿

﻿cos⁡3x2ex3cos⁡(ex3)\cos3x^2e^{x^3}\cos\left(e^{x^3}\right)cos3x2ex3cos(ex3)﻿

﻿−(4x−6)-\left(4x-6\right)−(4x−6)﻿

If ﻿y=f(u)y=f\left(u\right)y=f(u)﻿ and ﻿u=g(x)u=g\left(x\right)u=g(x)﻿. Calculate ﻿dydx\frac{dy}{dx}dxdy​﻿.

﻿dydu\frac{dy}{du}dudy​﻿

﻿dydxdxdu\frac{dy}{dx}\frac{dx}{du}dxdy​dudx​﻿

﻿dydududx\frac{dy}{du}\frac{du}{dx}dudy​dxdu​﻿

Use chain rule to find ﻿f′(x)f'\left(x\right)f′(x)﻿, if ﻿f(x)=tan⁡(1+x2)f\left(x\right)=\sqrt{\tan\left(1+x^2\right)}f(x)=tan(1+x2)​﻿.

﻿sec⁡2(x2+1)tan⁡(1+x2)\frac{\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(1+x^2\right)}}tan(1+x2)​sec2(x2+1)​﻿

﻿xsec⁡2(x2+1)tan⁡(1+x2)\frac{x\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(1+x^2\right)}}tan(1+x2)​xsec2(x2+1)​﻿

﻿xsec⁡2(x2+1)tan⁡(x2)\frac{x\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(x^2\right)}}tan(x2)​xsec2(x2+1)​﻿

Use chain rule to find ﻿f′(x)f'\left(x\right)f′(x)﻿, if ﻿f(x)=tan⁡tan⁡(x2)f\left(x\right)=\tan\tan\left(x^2\right)f(x)=tantan(x2)﻿.

﻿2xsec⁡(x2)2x\sec\left(x^2\right)2xsec(x2)﻿

﻿2sec⁡(x2)2\sec\left(x^2\right)2sec(x2)﻿

﻿2xsec⁡2(x2)2x\sec^2\left(x^2\right)2xsec2(x2)﻿

Use chain rule to find ﻿f′(x)f'\left(x\right)f′(x)﻿, if ﻿f(x)=sin⁡sin⁡(ex2)f\left(x\right)=\sin\sin\left(e^{x^2}\right)f(x)=sinsin(ex2)﻿.

﻿cos⁡x2ex3cos⁡(ex3)\cos x^2e^{x^3}\cos\left(e^{x^3}\right)cosx2ex3cos(ex3)﻿

﻿cos⁡3x2ex2cos⁡(ex2)\cos3x^2e^{x^2}\cos\left(e^{x^2}\right)cos3x2ex2cos(ex2)﻿

﻿cos⁡2xex2cos⁡(ex2)\cos2xe^{x^2}\cos\left(e^{x^2}\right)cos2xex2cos(ex2)﻿

Use chain rule to find ﻿f′(x)f'\left(x\right)f′(x)﻿, if ﻿f(x)=cos⁡cos⁡(tan⁡x)f\left(x\right)=\cos\cos\left(\tan x\right)f(x)=coscos(tanx)﻿.

﻿2xcos⁡(x2)2x\cos\left(x^2\right)2xcos(x2)﻿

﻿sin⁡sin⁡(tan⁡x)x\sin\sin\left(\tan x\right)xsinsin(tanx)x﻿

﻿−sin⁡sin⁡(tan⁡x)x-\sin\sin\left(\tan x\right)x−sinsin(tanx)x﻿

Use chain rule to find ﻿f′(x)f'\left(x\right)f′(x)﻿, if ﻿f(x)=sin⁡sin⁡(x2)f\left(x\right)=\sin\sin\left(x^2\right)f(x)=sinsin(x2)﻿.

﻿2xcos⁡(x2)2x\cos\left(x^2\right)2xcos(x2)﻿

﻿2cos⁡(x2)2\cos\left(x^2\right)2cos(x2)﻿

﻿xcos⁡(x2)x\cos\left(x^2\right)xcos(x2)﻿

Use chain rule to find ﻿dydx\frac{dy}{dx}dxdy​﻿, if ﻿y=f(u)=u+1y=f\left(u\right)=u+1y=f(u)=u+1﻿ and ﻿x=u+1ux=u+\frac{1}{u}x=u+u1​﻿.

﻿2u2u2 −1\frac{2u^2}{u^{2\ }-1}u2 −12u2​﻿

﻿u2u2 +1\frac{u^2}{u^{2\ }+1}u2 +1u2​﻿

﻿u2u2 −1\frac{u^2}{u^{2\ }-1}u2 −1u2​﻿

Use chain rule to find ﻿f′(x)f'\left(x\right)f′(x)﻿, if ﻿f(x)=sin⁡sin⁡(2x2−6x)f\left(x\right)=\sin\sin\left(2x^2-6x\right)f(x)=sinsin(2x2−6x)﻿.

﻿(4x−6)cos⁡cos⁡(2x2−6x)\left(4x-6\right)\cos\cos\left(2x^2-6x\right)(4x−6)coscos(2x2−6x)﻿

﻿cos⁡cos⁡(2x2−6x)\cos\cos\left(2x^2-6x\right)coscos(2x2−6x)﻿

﻿−(4x−6)-\left(4x-6\right)−(4x−6)﻿

Use chain rule to find ﻿f′(x)f'\left(x\right)f′(x)﻿, if ﻿f(x)=x+xf\left(x\right)=\sqrt{x+\sqrt{x}}f(x)=x+x​​﻿.

﻿2x4x+xx\frac{2\sqrt{x}}{4\sqrt{x+\sqrt{x}}\sqrt{x}}4x+x​​x​2x​​﻿

﻿2x+14x+xx\frac{2\sqrt{x}+1}{4\sqrt{x+\sqrt{x}}\sqrt{x}}4x+x​​x​2x​+1​﻿

﻿x+14x+xx\frac{\sqrt{x}+1}{4\sqrt{x+\sqrt{x}}\sqrt{x}}4x+x​​x​x​+1​﻿

Incorrect

Great!

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sin\sin\left(e^{x^3}\right)$ .

$\cos x^2e^{x^3}\cos\left(e^{x^3}\right)$

$\cos3x^2e^{x^3}\cos\left(e^{x^3}\right)$

$-\left(4x-6\right)$

If $y=f\left(u\right)$ and $u=g\left(x\right)$ . Calculate $\frac{dy}{dx}$ .

$\frac{dy}{du}$

$\frac{dy}{dx}\frac{dx}{du}$

$\frac{dy}{du}\frac{du}{dx}$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sqrt{\tan\left(1+x^2\right)}$ .

$\frac{\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(1+x^2\right)}}$

$\frac{x\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(1+x^2\right)}}$

$\frac{x\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(x^2\right)}}$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\tan\tan\left(x^2\right)$ .

$2x\sec\left(x^2\right)$

$2\sec\left(x^2\right)$

$2x\sec^2\left(x^2\right)$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sin\sin\left(e^{x^2}\right)$ .

$\cos x^2e^{x^3}\cos\left(e^{x^3}\right)$

$\cos3x^2e^{x^2}\cos\left(e^{x^2}\right)$

$\cos2xe^{x^2}\cos\left(e^{x^2}\right)$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\cos\cos\left(\tan x\right)$ .

$2x\cos\left(x^2\right)$

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

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

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sin\sin\left(x^2\right)$ .

$2x\cos\left(x^2\right)$

$2\cos\left(x^2\right)$

$x\cos\left(x^2\right)$

Use chain rule to find $\frac{dy}{dx}$ , if $y=f\left(u\right)=u+1$ and $x=u+\frac{1}{u}$ .

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

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

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

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sin\sin\left(2x^2-6x\right)$ .

$\left(4x-6\right)\cos\cos\left(2x^2-6x\right)$

$\cos\cos\left(2x^2-6x\right)$

$-\left(4x-6\right)$

Use chain rule to find $f'\left(x\right)$ , if $f\left(x\right)=\sqrt{x+\sqrt{x}}$ .

$\frac{2\sqrt{x}}{4\sqrt{x+\sqrt{x}}\sqrt{x}}$

$\frac{2\sqrt{x}+1}{4\sqrt{x+\sqrt{x}}\sqrt{x}}$

$\frac{\sqrt{x}+1}{4\sqrt{x+\sqrt{x}}\sqrt{x}}$