(Solved): Urgent help please Let \( w(x, y, z)=x^{2}+y^{2}+z^{2} \) where \( x=\sin (-2 t), y=\cos (-5 t), z=e ...

Let \( w(x, y, z)=x^{2}+y^{2}+z^{2} \) where \( x=\sin (-2 t), y=\cos (-5 t), z=e^{-2 t} \). Calculate \( \frac{d w}{d t} \) by first finding \( \frac{d x}{d t}, \frac{d y}{d t} \& \frac{d z}{d t} \) and using the chain rule. \( \frac{d x}{d t}= \) \( \frac{d y}{d t}= \) \( \frac{d z}{d t}= \) Now use the chain rule to calculate the following: \( \frac{d w}{d t}= \) \[ -4 x \cos (-2 t)-2 y^{2} \cos (-2 t)-2 z^{2} \cos (-2 t)+10 y \sin (-5 t)+5 x^{2} \sin (-5 t)+5 z^{2} \sin (-5 t)-4 z e^{-2 t}-2 x^{2} e^{-2 t}-2 \] syntax error. Check your variables - you might be using an incorrect one. Hint: Recall the chain rule: \( \frac{d w}{d t}=\left(\frac{\partial w}{\partial x} \cdot \frac{d x}{d t}\right)+\left(\frac{\partial w}{\partial y} \cdot \frac{d y}{d t}\right)+\left(\frac{\partial w}{\partial z} \cdot \frac{d z}{d t}\right) \)