Question

Tính đạo hàm của hàm số: \(y=x\sqrt{1-x^2}\)

Answer 1

\(y=x\sqrt{1-x^2}\)

=>\(y'=x'\cdot\sqrt{1-x^2}+x\cdot\left(\sqrt{1-x^2}\right)'\)

=>\(y'=\sqrt{1-x^2}+x\cdot\dfrac{\left(1-x^2\right)'}{2\sqrt{1-x^2}}\)

=>\(y'=\sqrt{1-x^2}+\dfrac{x\cdot\left(-2x\right)}{2\sqrt{1-x^2}}=\sqrt{1-x^2}-\dfrac{x}{\sqrt{1-x^2}}\)