derivative 5x^4(9-7x)^7

解答

导数

5 x^{4} (9 - 7 x)^{7}

5 (4 x^{3} (9 - 7 x)^{7} - 49 x^{4} (9 - 7 x)^{6})

求解步骤

\frac{d}{d x} (5 x^{4} (9 - 7 x)^{7})

将常数提出:

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

= 5 \frac{d}{d x} (x^{4} (9 - 7 x)^{7})

使用微分乘法定则:

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

f = x^{4}, g = (9 - 7 x)^{7}

= 5 (\frac{d}{d x} (x^{4}) (9 - 7 x)^{7} + \frac{d}{d x} ((9 - 7 x)^{7}) x^{4})

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

\frac{d}{d x} ((9 - 7 x)^{7}) = - 49 (9 - 7 x)^{6}

= 5 (4 x^{3} (9 - 7 x)^{7} + (- 49 (9 - 7 x)^{6}) x^{4})

化简

= 5 (4 x^{3} (9 - 7 x)^{7} - 49 x^{4} (9 - 7 x)^{6})

\int_{- π}^{π} 1

t an g e n t f (x) = x^{3} - 3 x^{2} - 8 x + 9

x \to \infty lim (5 + \frac{2}{x})

sec^{2} (x) d y + csc (y) d x = 0, y (\frac{π}{4}) = 0

x \to \infty + lim (3 + \frac{2}{x})