Question

Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105.

Answer 1

I have solved problem using basic concept of vector and differential Calculus. Each concept and step with proper reason is explained.Go through complete solution step by step and if u find it helpful then hit thumbs up and share feedback. Thanks

Solution! - Problema It iX baxed upon vector calculus. f (447) = ght fix -105 direction 다 the highext gradient of (moxt rapid) f will givea change. direction Gradiant d42) it = hof ti of i df Ze dn dy Te 7 (4) + 7 loctay) + ł ( -3 22) = y j + (0424)5 -ZZE

at ALOLU &(x, y, z) = 1 + 23 - 32 will give Now unit vector of above required direction به روز 1² +21² +2=37 3 or JT4 14 (4 + 54 +2 JT4 J4 is correct. option Problem-2 Itik baxed upon calculus precisely differential Calculus more f(x, y, z) xy + z-5 Where =rt as y=2r- sec(s) سكت 2 we are peed Now if we Total derivative of flacy, z) have find it termy of independent variablex which ts. It can be done al shown below using chain rute

df )ل Lac 5( 3( 2. ہ )4 02 ده 븷 رہے he ال 2 2 ) د ده ( 3 +ع) ه t + (ری)، اکسور و ا ر ن (s اه .۱ )ما JP 0 +م.لالا - 2( 8 + دے N + , F se xe he se ze = لا لا لا لال عدم کا لك) ا+ (زكامی شعاعی )X+ X.2699-secess) + JS کی و الم (د)حنه(ک) کربلا b G Anxwere ix option chain correct uxed to get 2) اله ix derivative