KB/S Solution: Proof [u(x + h) + v(x + h)] – [u(x) + v(x)] dr [u(x) + v(x)] = lim h→0 h и(х + h) — и(х) = lim v(x + h) – v(x) h h u(x + h) – u(x) lim v(x + h) – v(x) + lim du dx dv %3D h→0 h h0 h dx...

Extracted text: KB/S Solution: Proof [u(x + h) + v(x + h)] – [u(x) + v(x)] dr [u(x) + v(x)] = lim h→0 h и(х + h) — и(х) = lim v(x + h) – v(x) h h u(x + h) – u(x) lim v(x + h) – v(x) + lim du dx dv %3D h→0 h h0 h dx Differentiation Rules Home Work : 1. Prove the Derivative Product Rule? d dv du dx + v (uv) = u dx dx 2. Prove the Derivative Quotient Rule? du dx dv d dx и dx Differentiation Rules Example 7: Differentiate the following functions of x. (a) x³ 1 (d) „2+7 (b) x/3 (c) xV? (e) x~4/3 (f) (g) 10 Solution: (а) dx :(x³) = 3x³=1 = 3x² (b) 4 (12#) = e/-1 = d dr (xV2) = V2rV2-1 (c) %3D d (d) dx d 4 (x¬4) = -4x¬4-1 -4x-5 %3D = = - dx (e) (-/3) = -4/3)–1 = --73 m (VFF) = ) = (1 + )*/-1 = 2 + m)VF (B)을 (10)3 0 dx d (f) dx d yl+(#/2)-1 = dx d dx +


Extracted text: KB/S Solution: Proof [u(x + h) + v(x + h)] – [u(x) + v(x)] dr [u(x) + v(x)] = lim h→0 h и(х + h) — и(х) = lim v(x + h) – v(x) h h u(x + h) – u(x) lim v(x + h) – v(x) + lim du dx dv %3D h→0 h h0 h dx Differentiation Rules Home Work : 1. Prove the Derivative Product Rule? d dv du dx + v (uv) = u dx dx 2. Prove the Derivative Quotient Rule? du dx dv d dx и dx Differentiation Rules Example 7: Differentiate the following functions of x. (a) x³ 1 (d) „2+7 (b) x/3 (c) xV? (e) x~4/3 (f) (g) 10 Solution: (а) dx :(x³) = 3x³=1 = 3x² (b) 4 (12#) = e/-1 = d dr (xV2) = V2rV2-1 (c) %3D d (d) dx d 4 (x¬4) = -4x¬4-1 -4x-5 %3D = = - dx (e) (-/3) = -4/3)–1 = --73 m (VFF) = ) = (1 + )*/-1 = 2 + m)VF (B)을 (10)3 0 dx d (f) dx d yl+(#/2)-1 = dx d dx +