แก้โจทย์ d/dyleft(4x^7y^3z^8csc(y^4{z}^8)right)

$$\frac{d}{d y } \left(4 { x }^{ 7 } { y }^{ 3 } { z }^{ 8 } \csc ( { y }^{ 4 } { z }^{ 8 } ) \right)$$

หาค่า

$$4x^{7}z^{8}\left(-4y^{4}z^{8}\cos(y^{4}z^{8})+3\sin(y^{4}z^{8})\right)\times \left(\frac{y}{\sin(y^{4}z^{8})}\right)^{2}$$

$$z\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=\frac{\sqrt[4]{\pi n_{1}}}{z^{2}}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=-\frac{\sqrt[4]{\pi n_{1}}}{z^{2}}$$

หาอนุพันธ์ของ w.r.t. x

$$28x^{6}z^{8}\left(-4y^{4}z^{8}\cos(y^{4}z^{8})+3\sin(y^{4}z^{8})\right)\times \left(\frac{y}{\sin(y^{4}z^{8})}\right)^{2}$$

$$z\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=\frac{\sqrt[4]{\pi n_{1}}}{z^{2}}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=-\frac{\sqrt[4]{\pi n_{1}}}{z^{2}}$$