derivative of 10log_{10}(100x)

解答

\frac{d}{d x} (10 lo g_{10} (100 x))

\frac{10}{ln ( 10 ) x}

求解步骤

\frac{d}{d x} (10 lo g_{10} (100 x))

化简

10 lo g_{10} (100 x) : 10 (lo g_{10} (x) + 2)

= \frac{d}{d x} (10 (lo g_{10} (x) + 2))

将常数提出:

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

= 10 \frac{d}{d x} (lo g_{10} (x) + 2)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 10 (\frac{d}{d x} (lo g_{10} (x)) + \frac{d}{d x} (2))

\frac{d}{d x} (lo g_{10} (x)) = \frac{1}{x ln ( 10 )}

\frac{d}{d x} (2) = 0

= 10 (\frac{1}{x ln ( 10 )} + 0)

化简

10 (\frac{1}{x ln ( 10 )} + 0) : \frac{10}{ln ( 10 ) x}

= \frac{10}{ln ( 10 ) x}

\frac{d}{d x} (cos (2 x^{2} - 3))

d er i v a t i v e f (x) = \frac{x ^{2}}{2 + x}

a re a x^{2} - 2 x, x + 4

a re a y = x^{2} - 1, y = - x^{2} + 1

sin (2 x) d x + cos (3 y) d y = 0