derivative f(x)=ax^4+(a-9)x^2-9

解答

导数

f (x) = a x^{4} + (a - 9) x^{2} - 9

4 a x^{3} + 2 x (a - 9)

求解步骤

\frac{d}{d x} (a x^{4} + (a - 9) x^{2} - 9)

使用微分加减法定则:

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

= \frac{d}{d x} (a x^{4}) + \frac{d}{d x} ((a - 9) x^{2}) - \frac{d}{d x} (9)

\frac{d}{d x} (a x^{4}) = 4 a x^{3}

\frac{d}{d x} ((a - 9) x^{2}) = 2 x (a - 9)

\frac{d}{d x} (9) = 0

= 4 a x^{3} + 2 x (a - 9) - 0

化简

= 4 a x^{3} + 2 x (a - 9)

n = 1 \sum \infty \frac{3 n}{n ^{2} + 4}

\int cos^{2} (k x) d x

\int_{2}^{4} \frac{x}{x ^{2} + 6 x + 13} d x

n = 0 \sum \infty \frac{1}{n ^{2}}

\frac{\partial}{\partial x} (e^{6 x + 9 y})