derivative of arcsin(cos(x^2))

解答

\frac{d}{d x} (arcsin (cos (x^{2})))

- \frac{2 x sin ( x ^{2} )}{sin ^{2} ( x ^{2} )}

求解步骤

\frac{d}{d x} (arcsin (cos (x^{2})))

使用连锁律:

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

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

\frac{d}{d x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

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

化简

\frac{1}{1 - cos ^{2} ( x ^{2} )} (- sin (x^{2}) \cdot 2 x) : - \frac{2 x sin ( x ^{2} )}{sin ^{2} ( x ^{2} )}

= - \frac{2 x sin ( x ^{2} )}{sin ^{2} ( x ^{2} )}

\frac{d}{d x} (5 \cdot tan (2 x^{3}) + \frac{2}{x ^{2}})

\frac{d}{d x} ((x + 3) e^{6 x})

\frac{\partial}{\partial x} ((x + y^{2}) \cdot e^{- 4 x + 2 y})

im pl i c i t \frac{d y}{d x}, y = (9 + x)^{\frac{1}{x}}

x \to 5 lim ((34 - x^{2}) x)