The equation of a curve is $$\(2 \mathrm{e}^{2 x} y-y^{3}+4=0\)$$. Show that $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{4 \mathrm{e}^{2 x} y}{3 y^{2}-2 \mathrm{e}^{2 x}}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_22 Year：2020 Question No：5(a)
Answer:
Use product rule to differentiate \(2 \mathrm{e}^{2 x} y\)
Obtain \(4 \mathrm{e}^{2 x} y+2 \mathrm{e}^{2 x} \frac{\mathrm{d} y}{\mathrm{~d} x}\)
Differentiate \(-y^{3}\) to obtain \(-3 y^{2} \frac{\mathrm{d} y}{\mathrm{~d} x}\)
Obtain \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{4 \mathrm{e}^{2 x} y}{3 y^{2}-2 \mathrm{e}^{2 x}}\)
Obtain \(4 \mathrm{e}^{2 x} y+2 \mathrm{e}^{2 x} \frac{\mathrm{d} y}{\mathrm{~d} x}\)
Differentiate \(-y^{3}\) to obtain \(-3 y^{2} \frac{\mathrm{d} y}{\mathrm{~d} x}\)
Obtain \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{4 \mathrm{e}^{2 x} y}{3 y^{2}-2 \mathrm{e}^{2 x}}\)
Knowledge points:
2.4.1 use the derivatives of ,ln x,sin x,cos x,tan x, together with constant multiples, sums, differences and composites
2.4.2 differentiate products and quotients
2.4.3 find and use the first derivative of a function which is defined parametrically or implicitly.
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download