Selena Hardin

2023-02-24

How to find $f\prime \prime \left(x\right)=\mathrm{csc}x$?

daneetuhxxtj

For $f\left(x\right)=\mathrm{csc}x$, we have
$f\prime \left(x\right)=-\mathrm{csc}x\mathrm{cot}x=-\left[\mathrm{csc}x\mathrm{cot}x\right]$
The product rule will be required to differentiate this.
$f\prime \prime \left(x\right)=-\left[\left(-\mathrm{csc}x\mathrm{cot}x\right)\mathrm{cot}x+\left(\mathrm{csc}x\right)\left(-{\mathrm{csc}}^{2}x\right)\right]$
$f\prime \prime \left(x\right)=\mathrm{csc}x{\mathrm{cot}}^{2}x+{\mathrm{csc}}^{3}x$

Do you have a similar question?