derivative of 2x+1/(ln(x^2+e+1)-4)

解答

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

- \frac{2 x}{( x ^{2} + e ) ( ln ( x ^{2} + e ) + 1 ) ^{2}} + 2

求解步骤

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

使用微分加减法定则:

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

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

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

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

\frac{d}{d x} (4) = 0

= 2 - \frac{2 x}{( ln ( x ^{2} + e ) + 1 ) ^{2} ( x ^{2} + e )} - 0

化简

= - \frac{2 x}{( x ^{2} + e ) ( ln ( x ^{2} + e ) + 1 ) ^{2}} + 2

\frac{d}{d x} (5 6 x)

d er i v a t i v e \frac{x}{4} arcsin (x)

\frac{\partial}{\partial x} (\frac{1}{2 x ^{2}})

x \to 0 lim (\frac{10}{x})

\int_{l n (9)}^{l n (36)} e^{\frac{x}{2}} d x