dapatkan persamaan garis singgung yang melalui kurva xu^2 + y + akar x = x + 3 di titik (4,1)

Mari kita cari persamaan **garis singgung** kurva \(xu^2 + y + \sqrt{x} = x + 3\) di titik \( (4,1) \). Kita akan menggunakan konsep **turunan implisit** untuk menemukan gradien garis singgung. Berikut langkah-langkahnya:

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### Langkah 1: Turunkan persamaan kurva secara implisit
Persamaan yang diberikan adalah:  
\[
x u^2 + y + \sqrt{x} = x + 3
\]
Karena \(u = y\), maka bentuknya menjadi:
\[
x y^2 + y + \sqrt{x} = x + 3
\]

Untuk mencari gradien \(\frac{dy}{dx}\), kita turunkan setiap supli

Learn how to find the equation of the tangent line to the curve xu^2 + y + sqrt(x) = x + 3 at the point (4,1) using implicit differentiation. This solution includes step-by-step calculations, exploring key calculus concepts such as finding the derivative implicitly and determining the slope of the tangent line. Suitable for students in Grades 11-12 or early college courses.

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