derivative of (log_{10}(x)^2)

解答

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

\frac{2 lo g _{10} ( x )}{ln ( 10 ) x}

求解步骤

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

使用连锁律:

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

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

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

= 2 lo g_{10} (x) \frac{1}{x ln ( 10 )}

化简

2 lo g_{10} (x) \frac{1}{x ln ( 10 )} : \frac{2 lo g _{10} ( x )}{ln ( 10 ) x}

= \frac{2 lo g _{10} ( x )}{ln ( 10 ) x}

y^{^{''}} + 3 y = 5

y^{^{''}} + y = \frac{1}{2 k ^{2}} (1 + cos (2 t))

\frac{d}{d x} ((x^{5} + 1)^{4})

t an g e n t f (x) = \frac{1}{x}, at x = 81

t an g e n t arccos (x) + x, at x = 0