Question

Jawablah soal di bawah ini.

Answer 1

Jawab:

Penjelasan dengan langkah-langkah:

Answer 2

misal y = f(x)/g(x)

y = √(x/2-x)

  = x^1/2/(2-x)^1/2

f(x) = x^1/2

     = √x

g(x) = (2-x)^1/2

      = √2-x

f'(x) = 1/2x^-1/2

      = 1/2(1/x)^1/2

      = 1/2√x

      = √x/2x

g'(x) = 1/2(2-x)^-1/2  ×1×(-x⁰)+0

       = 1/2(1/(2-x)^1/2)×-1

       = -1/2(2-x)^1/2

       = -1/2√2-x

       = -√2-x/2(2-x)

       = -√(2-x)/4-2x

y' = (f'(x)×g(x)-f(x)×g'(x))/(g(x))²

   = ((√x/2x)(√(2-x))-(-√x(√(2-x)/4-2x)))/(√2-x)²

   = (√(x(2-x))/2x+√(x(2-x))/4-2x)/(2-x)

   = (√(2x-x²)/2x+√(2x-x²)/4-2x)/(2-x)

   = (√(2x-x²)(4-2x)+√(2x-x²)(2x))/(2x)(4-2x)(2-x)

   = (4√(2x-x²)-2x√(2x-x²)+2x√(2x-x²))/(2x)(4-2x)(2-x)

   = (4√(2x-x²))/(2x)(4-2x)(2-x)

   = (4√(2x-x²))/(2x)(4-2x)(2-x)×√(2x-x²)/√(2x-x²)

   = (2x-x²)(4)/4(x)(2-x)(2-x)√(2x-x²)

   = (2x-x²)/(2x-x²)(2-x)√(2x-x²)

   = 1/(2-x)√(2x-x²)

C