derivative f(y)=6x^2ln(x^2)

解答

导数

f (y) = 6 x^{2} ln (x^{2})

6 (2 x ln (x^{2}) + 2 x)

求解步骤

\frac{d}{d x} (6 x^{2} ln (x^{2}))

将常数提出:

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

= 6 \frac{d}{d x} (x^{2} ln (x^{2}))

使用微分乘法定则:

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

f = x^{2}, g = ln (x^{2})

= 6 (\frac{d}{d x} (x^{2}) ln (x^{2}) + \frac{d}{d x} (ln (x^{2})) x^{2})

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

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

= 6 (2 x ln (x^{2}) + \frac{2}{x} x^{2})

\frac{2}{x} x^{2} = 2 x

= 6 (2 x ln (x^{2}) + 2 x)

\frac{d}{d x} (\frac{1}{( x ^{2} + 1 ) x ^{2} + 1})

\frac{\partial}{\partial x} (e^{- x a})

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = a, y^{^{'}} (0) = - 5

\int (t^{2} - 6)^{2} d t

d er i v a t i v e f (x) = \frac{x ^{2} + 5 x}{x + 2}