g'(x) dari g(θ) = (2 sin⁡ θ - cos ⁡θ)/ (sin⁡ ⁡θ + 3 cos⁡ θ) adalah *

Halo Yuva, kakak bantu jawab ya. Jawaban soal ini adalah g'( ⁡θ) = 7/(3sin(2θ) +4cos(2θ) + 5) Ingat konsep: 1. Jika f(x) = sin x, maka turunan pertamanya adalah f’(x) = cosx 3. Jika f(x) = cos x, maka turunan pertamanya adalah f’(x) = -sin x 4. Jika f(x) = u(x) + v(x), maka turunan pertamanya adalah f’(x) = u’(x) + v’(x) 5. Jika f(x) = u(x) / v(x), maka turunan pertamanya adalah f’(x) =( u’(x)v(x) - u(x)v’(x))/(v(x))^2 5.Jika f(x) =k u(x), maka turunan pertamanya adalah f’(x) = k u’(x) 6. sin2x = 2sinxcosx 7.cos2x = 1- 2sin^2 (x) Dari soal akan dicari g'( ⁡θ) jika g(θ) = (2 sin⁡ θ - cos ⁡θ)/ (sin⁡ ⁡θ + 3 cos⁡ θ). Misal u(⁡θ ) = 2 sin⁡ θ - cos ⁡θ dan v(θ ) = sin⁡ ⁡θ + 3 cos⁡ θ, maka: u'(⁡θ ) = 2 cos⁡ θ -(-sin ⁡θ) u'(⁡θ ) = 2 cos⁡ θ + sin ⁡θ v'(θ ) = cos⁡ ⁡θ - 3 sin θ u'(⁡θ )v(⁡θ ) = ( 2 cos⁡ θ + sin ⁡θ)( sin⁡ ⁡θ + 3 cos⁡ θ) u'(⁡θ )v(⁡θ ) = 2 sin⁡ ⁡θcos⁡ θ + 6 cos^2 ⁡(θ) + sin^2 (⁡ θ) + 3sin⁡ ⁡θcos⁡ θ u'(⁡θ )v(⁡θ ) = 5 sin⁡ ⁡θcos⁡ θ + 6 cos^2 ⁡(θ) + sin^2 (⁡ θ) u(⁡θ )v'(⁡θ )=(2 sin⁡ θ - cos ⁡θ)(cos⁡ ⁡θ - 3 sin θ) u(⁡θ )v'(⁡θ )=2 sin⁡ θcos⁡ ⁡θ - 6sin^2(θ) -cos^2 (θ) + 3sin⁡ θcos⁡ ⁡θ u(⁡θ )v'(⁡θ )=5sin⁡ θcos⁡ ⁡θ - 6sin^2(θ) -cos^2 (θ) u'(⁡θ )v(⁡θ )- u(⁡θ )v'(⁡θ )=5 sin⁡ ⁡θcos⁡ θ + 6 cos^2 ⁡(θ) + sin^2 (⁡ θ)-(5sin⁡ θcos⁡ ⁡θ - 6sin^2(θ) -cos^2(θ) ) u'(⁡θ )v(⁡θ )- u(⁡θ )v'(⁡θ )=5 sin⁡ ⁡θcos⁡ θ + 6 cos^2 ⁡(θ) + sin^2 (⁡ θ)-5sin⁡ θcos⁡ ⁡θ +6sin^2(θ) +cos^2(θ) u'(⁡θ )v(⁡θ )- u(⁡θ )v'(⁡θ )= 7cos^2 ⁡(θ) + 7sin^2 (⁡ θ) u'(⁡θ )v(⁡θ )- u(⁡θ )v'(⁡θ )= 7(cos^2 ⁡(θ) + sin^2 (⁡ θ)) u'(⁡θ )v(⁡θ )- u(⁡θ )v'(⁡θ )= 7.1 u'(⁡θ )v(⁡θ )- u(⁡θ )v'(⁡θ )= 7 (v(⁡θ ))^2= sin⁡ ⁡θ + 3 cos⁡ θ)^2 (v(⁡θ ))^2= sin⁡^2(θ) + 6sinθcosθ + 9cos^2(θ) (v(⁡θ ))^2= sin⁡^2(θ) + 3sin(2θ) + 9cos^2(θ) (v(⁡θ ))^2= sin⁡^2(θ) + 3sin(2θ) + 9(1-sin^2(θ)) (v(⁡θ ))^2= sin⁡^2(θ) + 3sin(2θ) + 9-9sin^2(θ) (v(⁡θ ))^2= 3sin(2θ) + 9-8sin^2(θ) (v(⁡θ ))^2= 3sin(2θ) + 5 +4(1-2sin^2(θ)) (v(⁡θ ))^2= 3sin(2θ) + 5 +4cos(2θ) (v(⁡θ ))^2= 3sin(2θ) +4cos(2θ) + 5 Didapat: g'( ⁡θ) = (u'(⁡θ )v(⁡θ )- u(⁡θ )v'(⁡θ ))/((v(⁡θ ))^2 g'( ⁡θ) = 7/(3sin(2θ) +4cos(2θ) + 5) Jadi, g'( ⁡θ) = 7/(3sin(2θ) +4cos(2θ) + 5) Semoga membantu ya:)