derivative of 6x^2+15xy+3y^2

解答

\frac{d}{d x} (6 x^{2} + 15 x y + 3 y^{2})

12 x + 15 (y + x \frac{d y}{d x}) + 6 y \frac{d y}{d x}

求解步骤

\frac{d}{d x} (6 x^{2} + 15 x y + 3 y^{2})

使用微分加减法定则:

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

= \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (15 x y) + \frac{d}{d x} (3 y^{2})

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (15 x y) = 15 (y + x \frac{d y}{d x})

\frac{d}{d x} (3 y^{2}) = 6 y \frac{d y}{d x}

= 12 x + 15 (y + x \frac{d y}{d x}) + 6 y \frac{d y}{d x}

\int (e^{x} x) d x

x \to \infty lim (\frac{( e ^{2 x} - 8 - 19 x )}{( 19 x ) ^{2}})

y^{^{''}} + 49 y = 0

\int 64 sin^{2} (x) d x

t an g e n t f (x) = x^{3} - 11 x, at x = 3