Pertanyaan

.Diketahui fungsi implisit y^2=x^3 maka nilai y' di titik (1,2) adalah __ Select one or more: a. 3/4 b. 4/5 C. 5/6 d. 2/3 e. 1/2

Solusi

Terverifikasi Ahli
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Dhaval elit · Tutor selama 8 tahun

Jawaban

d. 2/3

Penjelasan

The expression y^2 = x^3 is an implicit function in the form of f(x,y)=0. Differentiating it implicitly w.r.t x we begin by differentiating both sides with respect to 'x' by using the chain rule. Resulting in 2yy' = 3x^2. Solving for y′ we achieve y′ = (3x^2)/(2y). To find y' at the point (1,2), we substitute x=1 and y=2 into that equation.