Gray Brooks
12/25/2023 · Elementary School
derivar \( x=2 e^{t} \) \( y=e^{-\frac{t}{2}} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Para derivar las funciones \( x = 2 e^{t} \) y \( y = e^{-\frac{t}{2}} \) con respecto a \( t \), vamos a calcular las derivadas \( \frac{dx}{dt} \) y \( \frac{dy}{dt} \).
1. **Derivada de \( x \)**:
\[
x = 2 e^{t}
\]
Usando la regla de la derivada de la exponencial, tenemos:
\[
\frac{dx}{dt} = 2 e^{t}
\]
2. **Derivada de \( y \)**:
\[
y = e^{-\frac{t}{2}}
\]
Aplicando la regla de la cadena, la derivada es:
\[
\frac{dy}{dt} = e^{-\frac{t}{2}} \cdot \left(-\frac{1}{2}\right) = -\frac{1}{2} e^{-\frac{t}{2}}
\]
Por lo tanto, las derivadas son:
\[
\frac{dx}{dt} = 2 e^{t}
\]
\[
\frac{dy}{dt} = -\frac{1}{2} e^{-\frac{t}{2}}
\]
Quick Answer
\[
\frac{dx}{dt} = 2 e^{t}
\]
\[
\frac{dy}{dt} = -\frac{1}{2} e^{-\frac{t}{2}}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit