Hilton Chan
09/07/2023 · Senior High School
11. If \( y \) is a function of \( x \) and \( x=\frac{e^{t}}{e^{t}+1} \) Show that \( \frac{d y}{d x}=x(1-x) \frac{d y}{d x} \) 12. If \( y=\sec x \), prove that \( y \frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2}+y^{4} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Quick Answer
For problem 11, we have shown that \( \frac{dy}{dx} = x(1-x) \frac{dy}{dt} \). For problem 12, we have proven that \( y \frac{d^2 y}{dx^2} = \left( \frac{dy}{dx} \right)^2 + y^4 \).
Step-by-step Solution
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