derivative 2t(3t^2-7)^5

解答

导数

2 t (3 t^{2} - 7)^{5}

2 ((3 t^{2} - 7)^{5} + 30 t^{2} (3 t^{2} - 7)^{4})

求解步骤

\frac{d}{d t} (2 t (3 t^{2} - 7)^{5})

将常数提出:

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

= 2 \frac{d}{d t} (t (3 t^{2} - 7)^{5})

使用微分乘法定则:

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

f = t, g = (3 t^{2} - 7)^{5}

= 2 (\frac{d t}{d t} (3 t^{2} - 7)^{5} + \frac{d}{d t} ((3 t^{2} - 7)^{5}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} ((3 t^{2} - 7)^{5}) = 30 t (3 t^{2} - 7)^{4}

= 2 (1 \cdot (3 t^{2} - 7)^{5} + 30 t (3 t^{2} - 7)^{4} t)

化简

2 (1 \cdot (3 t^{2} - 7)^{5} + 30 t (3 t^{2} - 7)^{4} t) : 2 ((3 t^{2} - 7)^{5} + 30 t^{2} (3 t^{2} - 7)^{4})

= 2 ((3 t^{2} - 7)^{5} + 30 t^{2} (3 t^{2} - 7)^{4})

x \to 4 lim (5 x - 4)

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

d er i v a t i v e y = (3 x + 2) x^{2}

\frac{d}{d x} (2 x^{2} + y^{2} - ln (x y^{2}))

t an g e n t y = 2 + \frac{1}{x}, (1, 3)