derivative of sqrt(5)x^5{f}(x)

解答

\frac{d}{d x} (5 x^{5} f (x))

5 (5 x^{4} f (x) + \frac{d}{d x} (f (x)) x^{5})

求解步骤

\frac{d}{d x} (5 x^{5} f (x))

将常数提出:

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

= 5 \frac{d}{d x} (x^{5} f (x))

使用微分乘法定则:

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

f = x^{5}, g = f (x)

= 5 (\frac{d}{d x} (x^{5}) f (x) + \frac{d}{d x} (f (x)) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 5 (5 x^{4} f (x) + \frac{d}{d x} (f (x)) x^{5})

y^{^{'}} = e^{t + y}, y (0) = 0

\int 5 e^{3 x + 7} d x

\int_{0}^{5} (x^{2} - 5 x) d x

n = 0 \sum \infty (- 1)^{n} 2

a re a \frac{21}{x ^{3}}, 1, 1000