Mathematics 1 Deneme Sınavı Sorusu #1233100

9u^5-12u⁴+5u³+6u²-2u

9u⁵+12u⁴-5u³-6u²+2u

6u⁵-5u³-6u²+2u

6u⁵+5u⁴-5u³-6u²+2u

u⁵+12u⁴-u³-6u²+2

Yanıt Açıklaması:

dz/du=(dz/dx)*(dx/du)+(dz/dy)*(dy/du)

Since z=(x+y)², dz/dx=2x+2y and dz/dy=2x+2y

Since y=u³, dy/du=3u²

x=u²-u, dx/du=2u-1

By substitution

dz/du=(2x+2y)(2u-1)+(2x+2y)3u²=(2x+3y)(3u²+2u-1)=(2(u²-u)+3u³)(3u²+2u-1)=(2u²-2u+3u³)(3u²+2u-1)=9u⁵+12u⁴-5u³-6u²+2u

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