derivative f(x)=4e^xcos(x)

解答

导数

f (x) = 4 e^{x} cos (x)

4 (e^{x} cos (x) - e^{x} sin (x))

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

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

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

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

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

= 4 (e^{x} cos (x) + (- sin (x)) e^{x})

化简

= 4 (e^{x} cos (x) - e^{x} sin (x))

\int_{2}^{3} t sin (π t) d t

\int \frac{( x ^{5} - x ^{3} + 2 x )}{x ^{4}} d x

l a pl a ce t r an s f or m 1 - e^{- t}

\int \frac{6 x ^{3} + 8 x}{x ^{4} - 16} d x

\frac{d y}{d x} = 6 x (y - 1)^{\frac{2}{3}}