derivative f(x)=x*ln(x)

解答

导数

f (x) = x \cdot ln (x)

ln (x) + 1

求解步骤

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

使用微分乘法定则:

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

f = x, g = ln (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot ln (x) + \frac{1}{x} x

化简

1 \cdot ln (x) + \frac{1}{x} x : ln (x) + 1

= ln (x) + 1

\frac{\partial}{\partial x} (x^{8} + 6 x y^{7})

d er i v a t i v e 6 + \frac{1}{x ^{2}}

y^{^{''}} + 4 y = 3 cos (2 t) - 5 sin (2 t)

t an g e n t y = x^{4} - 4 x^{2} + 10, at x = 1

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