derivative (4e^x)/(cos(x))

解答

导数

\frac{4 e ^{x}}{cos ( x )}

4 sec (x) (e^{x} + e^{x} tan (x))

求解步骤

\frac{d}{d x} (\frac{4 e ^{x}}{cos ( x )})

化简

\frac{4 e ^{x}}{cos ( x )} : 4 e^{x} sec (x)

= \frac{d}{d x} (4 e^{x} sec (x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (e^{x} sec (x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = sec (x)

= 4 (\frac{d}{d x} (e^{x}) sec (x) + \frac{d}{d x} (sec (x)) e^{x})

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

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

= 4 (e^{x} sec (x) + sec (x) tan (x) e^{x})

化简

4 (e^{x} sec (x) + sec (x) tan (x) e^{x}) : 4 sec (x) (e^{x} + e^{x} tan (x))

= 4 sec (x) (e^{x} + e^{x} tan (x))

y^{^{''}} - 4 y^{^{'}} + 13 y = 2 e^{x}

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