derivative f(x)=\sqrt[4]{x}sin(x)

解答

导数

f (x) = 4 x sin (x)

\frac{sin ( x )}{4 x ^{\frac{3}{4}}} + 4 x cos (x)

求解步骤

\frac{d}{d x} (4 x sin (x))

使用微分乘法定则:

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

f = 4 x, g = sin (x)

= \frac{d}{d x} (4 x) sin (x) + \frac{d}{d x} (sin (x)) 4 x

\frac{d}{d x} (4 x) = \frac{1}{4 x ^{\frac{3}{4}}}

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

= \frac{1}{4 x ^{\frac{3}{4}}} sin (x) + cos (x) 4 x

\frac{1}{4 x ^{\frac{3}{4}}} sin (x) = \frac{sin ( x )}{4 x ^{\frac{3}{4}}}

= \frac{sin ( x )}{4 x ^{\frac{3}{4}}} + 4 x cos (x)

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