derivative y=e^4x^2+1

解答

导数

y = e^{4} x^{2} + 1

2 e^{4} x

求解步骤

\frac{d}{d x} (e^{4} x^{2} + 1)

使用微分加减法定则:

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

= \frac{d}{d x} (e^{4} x^{2}) + \frac{d}{d x} (1)

\frac{d}{d x} (e^{4} x^{2}) = 2 e^{4} x

\frac{d}{d x} (1) = 0

= 2 e^{4} x + 0

化简

= 2 e^{4} x

\frac{\partial}{\partial y} (3 x^{2} y^{2} + 1)

\frac{x}{( 1 + x ^{2} )} d x + \frac{y}{( 1 + y ^{2} )} d y = 0

f (x) = \frac{2 x}{1 + x ^{2}}

63 x^{2} y^{^{''}} + 14 x (x - 9) y^{^{'}} - 14 (x - 9) y = - 2 x^{3}

t an g e n t y = x^{2} - x