derivative (|x|)/(sqrt(5-x^2))

解答

导数

\frac{∣ x ∣}{5 - x ^{2}}

\frac{5 x}{∣ x ∣ ( 5 - x ^{2} ) - x ^{2} + 5}

求解步骤

\frac{d}{d x} (\frac{∣ x ∣}{5 - x ^{2}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ∣ x ∣ ) 5 - x ^{2} - \frac{d}{d x} ( 5 - x ^{2} ) ∣ x ∣}{( 5 - x ^{2} ) ^{2}}

\frac{d}{d x} (∣ x ∣) = \frac{x}{∣ x ∣}

\frac{d}{d x} (5 - x^{2}) = - \frac{x}{5 - x ^{2}}

= \frac{\frac{x}{∣ x ∣} 5 - x ^{2} - ( - \frac{x}{5 - x ^{2}} ) ∣ x ∣}{( 5 - x ^{2} ) ^{2}}

化简

\frac{\frac{x}{∣ x ∣} 5 - x ^{2} - ( - \frac{x}{5 - x ^{2}} ) ∣ x ∣}{( 5 - x ^{2} ) ^{2}} : \frac{5 x}{∣ x ∣ ( 5 - x ^{2} ) - x ^{2} + 5}

= \frac{5 x}{∣ x ∣ ( 5 - x ^{2} ) - x ^{2} + 5}

x^{2} y d x - (x^{3} + y^{3}) d y = 0

d er i v a t i v e e^{2 - 5 x}

ma c l a u r in x^{2} e^{- x}

\int cos (e^{x}) d x

\int (1 - cos (x))^{\frac{1}{2}} d x