derivative of (3cos(x)(ln(1+x)))

解答

\frac{d}{d x} ((3 cos (x)) (ln (1 + x)))

3 (- sin (x) ln (1 + x) + \frac{cos ( x )}{1 + x})

求解步骤

\frac{d}{d x} ((3 cos (x)) (ln (1 + x)))

将常数提出:

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

= 3 \frac{d}{d x} (cos (x) ln (1 + x))

使用微分乘法定则:

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

f = cos (x), g = ln (1 + x)

= 3 (\frac{d}{d x} (cos (x)) ln (1 + x) + \frac{d}{d x} (ln (1 + x)) cos (x))

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

\frac{d}{d x} (ln (1 + x)) = \frac{1}{1 + x}

= 3 ((- sin (x)) ln (1 + x) + \frac{1}{1 + x} cos (x))

化简

3 ((- sin (x)) ln (1 + x) + \frac{1}{1 + x} cos (x)) : 3 (- sin (x) ln (1 + x) + \frac{cos ( x )}{1 + x})

= 3 (- sin (x) ln (1 + x) + \frac{cos ( x )}{1 + x})

\int \frac{7 sec ^{2} ( 2 x )}{3 - 5 tan ( 2 x )} d x

\int arcsinh (x) d x

x \to + 0 + lim (x^{12} ln (x))

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

s l o p e (- 3.7) (0.3)