derivative of sin(xsqrt(x))

解答

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

x cos (x) + \frac{sin ( x )}{2 x}

求解步骤

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

使用微分乘法定则:

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

f = sin (x), g = x

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

= cos (x) x + \frac{1}{2 x} sin (x)

\frac{1}{2 x} sin (x) = \frac{sin ( x )}{2 x}

= x cos (x) + \frac{sin ( x )}{2 x}

t an g e n t f (x) = 7 e^{x} + 4 x, at x = 0

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