Hàm số \(y=\left(1-x^2\right)^{-\dfrac{1}{4}}\) có đạo hàm là
\(y'=-\dfrac{1}{4}\left(1-x^2\right)^{-\dfrac{5}{4}}\).\(y'=-\dfrac{5}{2}x\left(1-x^2\right)^{-\dfrac{5}{4}}\).\(y'=\dfrac{5}{2}x\left(1-x^2\right)^{-\dfrac{5}{4}}\).\(y'=\dfrac{1}{2}x\left(1-x^2\right)^{-\dfrac{5}{4}}\).Hướng dẫn giải:\(y=\left(1-x^2\right)^{-\frac{1}{4}}\)
\(y'=\left(-\dfrac{1}{4}\right)\left(1-x^2\right)'\left(1-x^2\right)^{-\frac{1}{4}-1}\)\(=-\dfrac{1}{4}\left(-2x\right)\left(1-x^2\right)^{-\frac{5}{4}}\)\(=\dfrac{1}{2}x\left(1-x^2\right)^{-\frac{5}{4}}\).