My professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text. Derivatives3+x(a) Let f(x) =-, x + 3. Evaluate f'(2) from the definition.3 — х4.1.f(2 + h) – f(2)1(5+hlim1 6h- 5 = lim6f'(2) = lim- = lim6.hh→0 h1-hh→0 h 1-h h→0 1-hh→0Note: By using rules of differentiation we find(3 - x) dxf'(x) = -d(3 + x) – (3 + x):d(3— х)dx(3 – x) (1) – (3 + x) (-1)(3— х)2(3- х)2(3 — х)?at all points x where the derivative exists. Putting x= 2, we find f'(2) = 6. Although such rules are often useful,one must be careful not to apply them indiscriminately (see Problem 4.5).(b) Let f(x) = /2x – 1. Evaluate f'(5) from the definition.f'(5) = limh→0f(5+ h) – f(5)9+2h – 3limhh→0h9+2h - 39 +2h +39 + 2h – 921limlimh→0 h (/9 +2h +3dBy using rules of differentiation we find f'(x) =dxlim9+2h +31h9+2h +33h→0h→0(2x – 1)/2- (2x – 1)-1/2 d(2x – 1) =dx21(2x – 1)-1/2. Then f'(5) = 9-1/2 =.3

Name: My professor says I have to explain the steps in the solved problems i
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: My professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text. Derivatives3+x(a) Let f(x) =-, x + 3. Evaluate f'(2) from the definition.3 — х4.1.f(2 + h) – f(2)1(5+hlim1 6h- 5 = lim6f