derivative (2q^2-3)^6(5q+4)^3

解答

导数

(2 q^{2} - 3)^{6} (5 q + 4)^{3}

24 q (2 q^{2} - 3)^{5} (5 q + 4)^{3} + 15 (5 q + 4)^{2} (2 q^{2} - 3)^{6}

求解步骤

\frac{d}{d q} ((2 q^{2} - 3)^{6} (5 q + 4)^{3})

使用微分乘法定则:

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

f = (2 q^{2} - 3)^{6}, g = (5 q + 4)^{3}

= \frac{d}{d q} ((2 q^{2} - 3)^{6}) (5 q + 4)^{3} + \frac{d}{d q} ((5 q + 4)^{3}) (2 q^{2} - 3)^{6}

\frac{d}{d q} ((2 q^{2} - 3)^{6}) = 24 q (2 q^{2} - 3)^{5}

\frac{d}{d q} ((5 q + 4)^{3}) = 15 (5 q + 4)^{2}

= 24 q (2 q^{2} - 3)^{5} (5 q + 4)^{3} + 15 (5 q + 4)^{2} (2 q^{2} - 3)^{6}

in v erse l a pl a ce \frac{2}{s \cdot ( s ^{2} + 4 s + 8 )}

(2 y + 2 t - 3) d t + (4 y + 2 t - 1) d y = 0

x \to 5 lim (x^{2} + 2 x - 3)

d er i v a t i v e f (x) = ln (4 x + 7)

\frac{d}{d x} (y z (x))