题目

问三道微积分题目 急
find first derivative
x^3-xy+y^2=4
f(x)=sec^2tanx
f(x)=ln(x e^7x)

提问时间：2021-04-01

答案

郭敦顒回答：
（x^3-xy+y^2）′=3x^2-（xy）′+2y
∵（xy）′= y +x
∴（x^3-xy+y^2）′=3x^2－x＋y.
f(x) =sec^2tanx,应表为f(x)=sec^2xtanx,于是
f(x)′=（sec^2xtanx）′＝（sec^2x）′tanx＋sec^2x（tanx）′
＝2secx（secx）′tanx+sec^2xsec^2x
=2sec^2xtan^2x+1/cos^4x.
f(x)=ln(x e^7x)
f(x)′=[ln(x e^7x)]′=1/(x e^7x)′=1/[ e^7x+ x e^7x(7x)′]
=1/(e^7x+ 7x e^7x)