(\partial)/(\partial x)(1/(cos^2(x)))

解答

\frac{\partial}{\partial x} (\frac{1}{cos ^{2} ( x )})

2 sec^{2} (x) tan (x)

求解步骤

\frac{\partial}{\partial x} (\frac{1}{cos ^{2} ( x )})

化简

\frac{1}{cos ^{2} ( x )} : sec^{2} (x)

= \frac{\partial}{\partial x} (sec^{2} (x))

使用连锁律:

2 sec (x) \frac{\partial}{\partial x} (sec (x))

= 2 sec (x) \frac{\partial}{\partial x} (sec (x))

\frac{\partial}{\partial x} (sec (x)) = sec (x) tan (x)

= 2 sec (x) sec (x) tan (x)

化简

2 sec (x) sec (x) tan (x) : 2 sec^{2} (x) tan (x)

= 2 sec^{2} (x) tan (x)

\int x 3 x^{2} - 1 d x

\int x^{3} - \frac{4}{3 x} + \frac{9}{x} + 6 e^{x} d x

in v erse l a pl a ce \frac{1}{( s ^{2} - 9 )}

\frac{d y}{d x} + 2 x^{2} y = 11 x^{2}

\int \frac{e ^{2 x} + 1}{e ^{2 x} - 1} d x