derivative of log_{10}(x^3)

解答

\frac{d}{d x} (lo g_{10} (x^{3}))

\frac{3}{ln ( 10 ) x}

求解步骤

\frac{d}{d x} (lo g_{10} (x^{3}))

使用对数计算法则:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x ^{3} )}{ln ( 10 )})

将常数提出:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{3}))

使用连锁律:

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{3}} \cdot 3 x^{2}

化简

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{3}{ln ( 10 ) x}

= \frac{3}{ln ( 10 ) x}

t an g e n t y = x^{3} - 15 x, (2, - 22)

t an g e n t 9 + 5 x^{2} - 2 x^{3}

\int \frac{x ^{2} - 1}{x ^{4}} d x

16 y^{^{''}} + 7 y = 0

\frac{d}{d x} (1 - e^{x} + (e - 1) sin ((\frac{π}{2}) x))