Exercise
$\frac{d^5}{dx^5}\left(\tanh\left(x\right)\right)$
Step-by-step Solution
Intermediate steps
1
Find the ($1$) derivative
$\mathrm{sech}\left(x\right)^2$
Intermediate steps
2
Find the ($2$) derivative
$-2\mathrm{sech}\left(x\right)^2\mathrm{tanh}\left(x\right)$
Intermediate steps
3
Find the ($3$) derivative
$4\mathrm{sech}\left(x\right)^2\mathrm{tanh}\left(x\right)^2-2\mathrm{sech}\left(x\right)^{4}$
Intermediate steps
4
Find the ($4$) derivative
$-8\mathrm{sech}\left(x\right)^2\mathrm{tanh}\left(x\right)^{3}+16\mathrm{sech}\left(x\right)^{4}\mathrm{tanh}\left(x\right)$
Intermediate steps
5
Find the ($5$) derivative
$16\mathrm{sech}\left(x\right)^2\mathrm{tanh}\left(x\right)^{4}-88\mathrm{sech}\left(x\right)^{4}\mathrm{tanh}\left(x\right)^2+16\mathrm{sech}\left(x\right)^{6}$
Final answer to the exercise
$16\mathrm{sech}\left(x\right)^2\mathrm{tanh}\left(x\right)^{4}-88\mathrm{sech}\left(x\right)^{4}\mathrm{tanh}\left(x\right)^2+16\mathrm{sech}\left(x\right)^{6}$