Question
Part 2 of 5 Use the Chain Rule to find \( \frac{d z}{d t} \), where \( z=3 x \cos y, x=t^{5} \), and \( y=6 t^{4} \). Points: 0 of 1 \( \frac{\partial z}{\partial x}=3 \cos y \) (Type an expression using \( x \) and \( y \) as the variables.) \( \frac{d x}{d t}=\square \) (Type an expression using \( t \) as the variable.)
Ask by West Gibson. in the United States
Mar 17,2025
Upstudy AI Solution
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Answer
\(\frac{d x}{d t} = 5t^{4}\)
Solution
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To find \( \frac{dx}{dt} \) when \( x = t^5 \), we differentiate with respect to \( t \). Thus, \( \frac{d x}{d t} = 5t^4 \). Now, let's summarize the findings: 1. \( \frac{\partial z}{\partial x} = 3 \cos y \). 2. \( \frac{d x}{d t} = 5 t^4 \).
