derivative of arcsin(x/7)

解答

\frac{d}{d x} (arcsin (\frac{x}{7}))

\frac{1}{49 - x ^{2}}

求解步骤

\frac{d}{d x} (arcsin (\frac{x}{7}))

使用连锁律:

\frac{1}{1 - ( \frac{x}{7} ) ^{2}} \frac{d}{d x} (\frac{x}{7})

= \frac{1}{1 - ( \frac{x}{7} ) ^{2}} \frac{d}{d x} (\frac{x}{7})

\frac{d}{d x} (\frac{x}{7}) = \frac{1}{7}

= \frac{1}{1 - ( \frac{x}{7} ) ^{2}} \cdot \frac{1}{7}

化简

\frac{1}{1 - ( \frac{x}{7} ) ^{2}} \cdot \frac{1}{7} : \frac{1}{49 - x ^{2}}

= \frac{1}{49 - x ^{2}}

\frac{\partial}{\partial x} (x e^{x y} - \frac{x}{y ^{2}})

t an g e n t \frac{( 8 e ^{(9 x)} )}{( 5 x - 2 )}

\frac{d}{d x} (x e^{7 x})

\int (2 x + 1) d x

\frac{d}{d x} (3 x^{2} sin (4 x))