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The second derivative

Fill in the blank:
If $f\left(x\right)=x^4-3x^2+x$ . $f^{\left(2\right)}\left(x\right)=$ __________.

$20x^3-36x^2$

$120x-2$

$12x^2-6$

Fill in the blank:
If $f\left(x\right)=\sec^3x$ . $f^{\left(2\right)}\left(x\right)=$ __________.

$3\left(3x\tan^2x+x\right)$

$3\left(3x\tan^2x+xx\right)$

$-60\cos x+81x$

Fill in the blank:
If $f\left(x\right)=\ln\ln\left(\sin x\right)$ . Then find $f^{\left(2\right)}\left(x\right)$ .

$-\cos x$

$-x$

$x$

Find the second derivative of the function $y=x^{11}$ .

$6x^{10}$

$6x^9$

$110x^9$

Fill in the blank:
If $f\left(x\right)=\ln\ln\left(\sin5x\right)$ . Then find $f^{\left(2\right)}\left(x\right)$ .

$-25\sin5x$

$-255x$

$25\sin5x$

Find the second derivative of the function $y=x\cos x$ .

$-x\cos x-2\sin x$

$-35\cos2x+528\sin2x$

$176\cos2x-176x\sin2x$

Fill in the blank:
If $f\left(x\right)=\cot3x$ . Then find second derivative of $f\left(x\right)$ .

$8\cos3x$

$-9\sin3x$

$183x\cot3x$

What is the notation for 2nd derivative of $g\left(x\right)$ ?

$g\left(2x\right)$

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

$\frac{d^2}{dx^2}\left(g\left(x\right)\right)$

Find the second derivative of the function $y=x^{15}$ .

$12x^2$

$24x$

$210x^{13}$

Fill in the blank:
If $f\left(x\right)=\tan3x$ . Then find second derivative of $f\left(x\right)$ .

$-9\cos3x$

$183x\tan3x$

$81\sin3x$

Questions

Time

Score

The second derivative

Fill in the blank:If ﻿f(x)=x4−3x2+xf\left(x\right)=x^4-3x^2+xf(x)=x4−3x2+x﻿. ﻿f(2)(x)=f^{\left(2\right)}\left(x\right)=f(2)(x)=﻿ __________.

﻿20x3−36x220x^3-36x^220x3−36x2﻿

﻿120x−2120x-2120x−2﻿

﻿12x2−612x^2-612x2−6﻿

Fill in the blank:If ﻿f(x)=sec⁡3xf\left(x\right)=\sec^3xf(x)=sec3x﻿. ﻿f(2)(x)=f^{\left(2\right)}\left(x\right)=f(2)(x)=﻿ __________.

﻿3(3xtan⁡2x+x)3\left(3x\tan^2x+x\right)3(3xtan2x+x)﻿

﻿3(3xtan⁡2x+xx)3\left(3x\tan^2x+xx\right)3(3xtan2x+xx)﻿

﻿−60cos⁡x+81x-60\cos x+81x−60cosx+81x﻿

Fill in the blank:If ﻿f(x)=ln⁡ln⁡(sin⁡x)f\left(x\right)=\ln\ln\left(\sin x\right)f(x)=lnln(sinx)﻿. Then find ﻿f(2)(x)f^{\left(2\right)}\left(x\right)f(2)(x)﻿.

﻿−cos⁡x-\cos x−cosx﻿

﻿−x-x−x﻿

﻿xxx﻿

Find the second derivative of the function ﻿y=x11y=x^{11}y=x11﻿.

﻿6x106x^{10}6x10﻿

﻿6x96x^96x9﻿

﻿110x9110x^9110x9﻿

Fill in the blank:If ﻿f(x)=ln⁡ln⁡(sin⁡5x)f\left(x\right)=\ln\ln\left(\sin5x\right)f(x)=lnln(sin5x)﻿. Then find ﻿f(2)(x)f^{\left(2\right)}\left(x\right)f(2)(x)﻿.

﻿−25sin⁡5x-25\sin5x−25sin5x﻿

﻿−255x-255x−255x﻿

﻿25sin⁡5x25\sin5x25sin5x﻿

Find the second derivative of the function ﻿y=xcos⁡xy=x\cos xy=xcosx﻿.

﻿−xcos⁡x−2sin⁡x-x\cos x-2\sin x−xcosx−2sinx﻿

﻿−35cos⁡2x+528sin⁡2x-35\cos2x+528\sin2x−35cos2x+528sin2x﻿

﻿176cos⁡2x−176xsin⁡2x176\cos2x-176x\sin2x176cos2x−176xsin2x﻿

Fill in the blank:If ﻿f(x)=cot⁡3xf\left(x\right)=\cot3xf(x)=cot3x﻿. Then find second derivative of ﻿f(x)f\left(x\right)f(x)﻿.

﻿8cos⁡3x8\cos3x8cos3x﻿

﻿−9sin⁡3x-9\sin3x−9sin3x﻿

﻿183xcot⁡3x183x\cot3x183xcot3x﻿

What is the notation for 2nd derivative of ﻿g(x)g\left(x\right)g(x)﻿?

﻿g(2x)g\left(2x\right)g(2x)﻿

﻿g2(x)g^2\left(x\right)g2(x)﻿

﻿d2dx2(g(x))\frac{d^2}{dx^2}\left(g\left(x\right)\right)dx2d2​(g(x))﻿

Find the second derivative of the function ﻿y=x15y=x^{15}y=x15﻿.

﻿12x212x^212x2﻿

﻿24x24x24x﻿

﻿210x13210x^{13}210x13﻿

Fill in the blank:If ﻿f(x)=tan⁡3xf\left(x\right)=\tan3xf(x)=tan3x﻿. Then find second derivative of ﻿f(x)f\left(x\right)f(x)﻿.

﻿−9cos⁡3x-9\cos3x−9cos3x﻿

﻿183xtan⁡3x183x\tan3x183xtan3x﻿

﻿81sin⁡3x81\sin3x81sin3x﻿

Incorrect

Great!

Fill in the blank:
If $f\left(x\right)=x^4-3x^2+x$ . $f^{\left(2\right)}\left(x\right)=$ __________.

$20x^3-36x^2$

$120x-2$

$12x^2-6$

Fill in the blank:
If $f\left(x\right)=\sec^3x$ . $f^{\left(2\right)}\left(x\right)=$ __________.

$3\left(3x\tan^2x+x\right)$

$3\left(3x\tan^2x+xx\right)$

$-60\cos x+81x$

Fill in the blank:
If $f\left(x\right)=\ln\ln\left(\sin x\right)$ . Then find $f^{\left(2\right)}\left(x\right)$ .

$-\cos x$

$-x$

$x$

Find the second derivative of the function $y=x^{11}$ .

$6x^{10}$

$6x^9$

$110x^9$

Fill in the blank:
If $f\left(x\right)=\ln\ln\left(\sin5x\right)$ . Then find $f^{\left(2\right)}\left(x\right)$ .

$-25\sin5x$

$-255x$

$25\sin5x$

Find the second derivative of the function $y=x\cos x$ .

$-x\cos x-2\sin x$

$-35\cos2x+528\sin2x$

$176\cos2x-176x\sin2x$

Fill in the blank:
If $f\left(x\right)=\cot3x$ . Then find second derivative of $f\left(x\right)$ .

$8\cos3x$

$-9\sin3x$

$183x\cot3x$

What is the notation for 2nd derivative of $g\left(x\right)$ ?

$g\left(2x\right)$

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

$\frac{d^2}{dx^2}\left(g\left(x\right)\right)$

Find the second derivative of the function $y=x^{15}$ .

$12x^2$

$24x$

$210x^{13}$

Fill in the blank:
If $f\left(x\right)=\tan3x$ . Then find second derivative of $f\left(x\right)$ .

$-9\cos3x$

$183x\tan3x$

$81\sin3x$