35 câu Dạng 2: Đạo hàm cấp cao

1.

10

4

16.

${y^{\text{'}}}^{\text{'}}=\frac{10}{{\left(x+2\right)}^2}$.

${y^{\text{'}}}^{\text{'}}=-\frac{5}{{\left(x+2\right)}^4}$.

${y^{\text{'}}}^{\text{'}}=-\frac{5}{{\left(x+2\right)}^3}$.

${y^{\text{'}}}^{\text{'}}=-\frac{10}{{\left(x+2\right)}^3}$.

-9

0.

9.

-3.

${y^{\text{'}}}^{\text{'}}=-2\cos 2x$.

${y^{\text{'}}}^{\text{'}}=-2\sin 2x$.

${y^{\text{'}}}^{\text{'}}=2\cos 2x$.

${y^{\text{'}}}^{\text{'}}=2\sin 2x$.

$y^{\text{'}}=\sin \left(x+\frac{\pi }{2}\right)$.

${y^{\text{'}}}^{\text{'}}=\sin \left(x+\pi \right)$.

${{y^{\text{'}}}^{\text{'}}}^{\text{'}}=\sin \left(x+\frac{3\pi }{2}\right)$.

$y^{\left(4\right)}=\sin \left(2\pi -x\right)$

$y^{\text{'}}=49\sin 7x+9\sin 3x$.

$y^{\text{'}}=-49\sin 7x-9\sin 3x$.

$y^{\text{'}}=\frac{49}{2}\sin 7x+\frac{9}{2}\sin 3x$.

$y^{\text{'}}=-\frac{49}{2}\sin 7x-\frac{9}{2}\sin 3x$.

$4y-{y^{\text{'}}}^{\text{'}}=0$.

$4y+{y^{\text{'}}}^{\text{'}}=0$

$y=y^{\text{'}}\tan 2x$.

$y^2+{\left(y^{\text{'}}\right)}^2=4$.

${y^{\text{'}}}^{\text{'}}=2+\frac{1}{{\left(1-x\right)}^2}$.

${y^{\text{'}}}^{\text{'}}=\frac{2}{{\left(1-x\right)}^3}$.

${y^{\text{'}}}^{\text{'}}=\frac{-2}{{\left(1-x\right)}^3}$.

${y^{\text{'}}}^{\text{'}}=\frac{2}{{\left(1-x\right)}^4}$.

$x=2$.

$x=4$.

$x=1$.

$x=3$.

$f^4\left(x\right)=24x-16\cos 2x$.

$f^4\left(x\right)=16\cos 2x$.

$f^4\left(x\right)=24x-8\sin 2x$.

$f^4\left(x\right)=24-16\cos 2x$.

Chỉ $\left(I\right)$.

Chỉ $\left(II\right)$.

Cả hai đều đúng

Cả hai đều sai.

${\left(y^{\text{'}}\right)}^2+y.{y^{\text{'}}}^{\text{'}}=-1$.

${\left(y^{\text{'}}\right)}^2+2y.{y^{\text{'}}}^{\text{'}}=1$

$y.{y^{\text{'}}}^{\text{'}}-{\left(y^{\text{'}}\right)}^2=1$

${\left(y^{\text{'}}\right)}^2+y.{y^{\text{'}}}^{\text{'}}=1$

3.

-3.

$\frac{3}{2}$.

0.

$P=4$.

$P=0$.

$P=-4$.

$P=-1$.

$x=\frac{\pi }{2}$.

$x=\mathrm{0,}x=\frac{\pi }{6}$.

$x=\mathrm{0,}x=\frac{\pi }{3}$.

$x=\mathrm{0,}x=\frac{\pi }{2}$.

${y^{\text{'}}}^{\text{'}}{y}^3+2=0$.

${y^{\text{'}}}^{\text{'}}{y}^3=2$.

${y^{\text{'}}}^{\text{'}}y+2{\left(y^{\text{'}}\right)}^2=0$.

${y^{\text{'}}}^{\text{'}}y=2{\left(y^{\text{'}}\right)}^2$

-8.

0.

8.

$16\sin 4x$.

$y^{\left(n\right)}={\left(-1\right)}^n\cos \left(2x+n\frac{\pi }{2}\right)$.

$y^{\left(n\right)}=2^n\cos \left(2x+\frac{\pi }{2}\right)$.

$y^{\left(n\right)}=2^{n+1}\cos \left(2x+n\frac{\pi }{2}\right)$.

$y^{\left(n\right)}=2^n\cos \left(2x+n\frac{\pi }{2}\right)$.

$y^n=\frac{{\left(-1\right)}^{n+1}\mathrm{.3.5...}\left(3n-1\right)}{\sqrt{{\left(2x+1\right)}^{2n-1}}}$.

$y^n=\frac{{\left(-1\right)}^{n-1}\mathrm{.3.5...}\left(2n-1\right)}{\sqrt{{\left(2x+1\right)}^{2n-1}}}$.

$y^n=\frac{{\left(-1\right)}^{n+1}\mathrm{.3.5...}\left(2n-1\right)}{\sqrt{{\left(2x+1\right)}^{2n+1}}}$.

$y^n=\frac{{\left(-1\right)}^{n+1}\mathrm{.3.5...}\left(2n-3\right)}{\sqrt{{\left(2x+1\right)}^{2n-1}}}$.

$y^{\left(n\right)}=\frac{5.{\left(-1\right)}^n.n!}{{\left(x-2\right)}^{n+1}}+\frac{3.{\left(-1\right)}^n.n!}{{\left(x-1\right)}^{n+1}}$.

$y^{\left(n\right)}=\frac{5.{\left(-1\right)}^n.n!}{{\left(x+2\right)}^{n+1}}-\frac{3.{\left(-1\right)}^n.n!}{{\left(x-1\right)}^{n+1}}$.

$y^{\left(n\right)}=\frac{5.{\left(-1\right)}^n.n!}{{\left(x-2\right)}^{n+1}}:\frac{3.{\left(-1\right)}^n.n!}{{\left(x-1\right)}^{n+1}}$.

$y^{\left(n\right)}=\frac{5.{\left(-1\right)}^n.n!}{{\left(x-2\right)}^{n+1}}-\frac{3.{\left(-1\right)}^n.n!}{{\left(x-1\right)}^{n+1}}$.

$y^{\left(n\right)}=\frac{{\left(-1\right)}^n\mathrm{.3.}n!}{{\left(x+3\right)}^{n+1}}+\frac{{\left(-1\right)}^n\mathrm{.2.}n!}{{\left(x+2\right)}^{n+1}}$.

$y^{\left(n\right)}=\frac{{\left(-1\right)}^n\mathrm{.3.}n!}{{\left(x+3\right)}^n}-\frac{{\left(-1\right)}^n\mathrm{.2.}n!}{{\left(x+2\right)}^n}$.

$y^{\left(n\right)}=\frac{{\left(-1\right)}^n\mathrm{.3.}n!}{{\left(x+3\right)}^{n-1}}-\frac{{\left(-1\right)}^n\mathrm{.2.}n!}{{\left(x+2\right)}^{n-1}}$.

$y^{\left(n\right)}=\frac{{\left(-1\right)}^n\mathrm{.3.}n!}{{\left(x+3\right)}^{n+1}}-\frac{{\left(-1\right)}^n\mathrm{.2.}n!}{{\left(x+2\right)}^{n+1}}$.

$f^{\left(2021\right)}\left(x\right)=-\cos \left(x+a+\frac{\pi }{2}\right)$.

$f^{\left(2021\right)}\left(x\right)=-\sin \left(x+a+\frac{\pi }{2}\right)$.

$f^{\left(2021\right)}\left(x\right)=\cos \left(x+a+\frac{\pi }{2}\right)$.

$f^{\left(2021\right)}\left(x\right)=\sin \left(x+a+\frac{\pi }{2}\right)$.

$y^{\left(n\right)}=2^{n+1}\sin \left(2x+n\frac{\pi }{2}\right)$.

$y^{\left(n\right)}=2^{n-1}\sin \left(2x+n\frac{\pi }{2}\right)$.

$y^{\left(n\right)}=2^n\sin \left(2x+\frac{\pi }{2}\right)$.

$y^{\left(n\right)}=2^n\sin \left(2x+n\frac{\pi }{2}\right)$.

454492.

2454493.

454491.

454490.

$\frac{1}{2^n}\sin \left(\frac{x}{2}+n\frac{\pi }{2}\right)$.

$\sin \left(\frac{x}{2}+n\frac{\pi }{2}\right)$.

$2^n\sin \left(\frac{x}{2}+n\frac{\pi }{2}\right)$.

$\frac{1}{2^n}\sin \left(\frac{x}{2}+n\pi \right)$.

$f^{\left(6\right)}\left(0\right)=-60480$

$f^{\left(6\right)}\left(0\right)=-34560$

$f^{\left(6\right)}\left(0\right)=60480$

$f^{\left(6\right)}\left(0\right)=34560$