Find the derivative of y.
-$$y = \operatorname { csch } \frac { 4 x } { 11 }$$
A) $\frac { 4 } { 11 } \operatorname { csch } \frac { 4 x } { 11 } \operatorname { coth } \frac { 4 x } { 11 }$
B) $- \frac { 4 } { 11 } \operatorname { csch } \frac { 4 x } { 11 } \operatorname { coth } \frac { 4 x } { 11 }$
C) $- \operatorname { csch } \frac { 4 x } { 11 } \operatorname { coth } \frac { 4 x } { 11 }$
D) $\operatorname { csch } \frac { 4 x } { 11 } \operatorname { coth } \frac { 4 x } { 11 }$

Question

Quizplus · Accepted Answer

The derivative of $y = \operatorname{csch}u$ with respect to $x$ is given by $\frac{dy}{dx} = -\operatorname{csch}u \cdot \operatorname{coth}u \cdot \frac{du}{dx}$. Here, $u = \frac{4x}{11}$, so $\frac{du}{dx} = \frac{4}{11}$. Substituting these values gives the derivative as $-\frac{4}{11} \operatorname{csch}\frac{4x}{11} \operatorname{coth}\frac{4x}{11}$.

Find the Derivative of Y y=csch⁡4x11y = \operatorname { csch } \frac { 4 x } { 11 }y=csch114x​

Find the Derivative of Y $y = \operatorname { csch } \frac { 4 x } { 11 }$