derivative f(x)=5x^2(x+47)

解答

导数

f (x) = 5 x^{2} (x + 47)

5 (3 x^{2} + 94 x)

求解步骤

\frac{d}{d x} (5 x^{2} (x + 47))

将常数提出:

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

= 5 \frac{d}{d x} (x^{2} (x + 47))

使用微分乘法定则:

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

f = x^{2}, g = x + 47

= 5 (\frac{d}{d x} (x^{2}) (x + 47) + \frac{d}{d x} (x + 47) x^{2})

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

\frac{d}{d x} (x + 47) = 1

= 5 (2 x (x + 47) + 1 \cdot x^{2})

化简

5 (2 x (x + 47) + 1 \cdot x^{2}) : 5 (3 x^{2} + 94 x)

= 5 (3 x^{2} + 94 x)

d er i v a t i v e y = csc (x)

d er i v a t i v e tan (x - y) = \frac{y}{1 + x ^{2}}

t an g e n t e^{x}

d er i v a t i v e f (x) = e^{x}

y = 8 x^{2}