Selena Hardin

2023-02-24

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

daneetuhxxtj

Beginner2023-02-25Added 8 answers

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.

$f\prime \prime \left(x\right)=-[(-\mathrm{csc}x\mathrm{cot}x)\mathrm{cot}x+\left(\mathrm{csc}x\right)(-{\mathrm{csc}}^{2}x)]$

$f\prime \prime \left(x\right)=\mathrm{csc}x{\mathrm{cot}}^{2}x+{\mathrm{csc}}^{3}x$

$f\prime \left(x\right)=-\mathrm{csc}x\mathrm{cot}x=-\left[\mathrm{csc}x\mathrm{cot}x\right]$

The product rule will be required to differentiate this.

$f\prime \prime \left(x\right)=-[(-\mathrm{csc}x\mathrm{cot}x)\mathrm{cot}x+\left(\mathrm{csc}x\right)(-{\mathrm{csc}}^{2}x)]$

$f\prime \prime \left(x\right)=\mathrm{csc}x{\mathrm{cot}}^{2}x+{\mathrm{csc}}^{3}x$