derivative of (5x^2+x+9tan(7x))

解

\frac{d}{d x} ((5 x^{2} + x + 9) tan (7 x))

(10 x + 1) tan (7 x) + sec^{2} (7 x) \cdot 7 (5 x^{2} + x + 9)

解答ステップ

\frac{d}{d x} ((5 x^{2} + x + 9) tan (7 x))

積の法則を適用:

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

f = 5 x^{2} + x + 9, g = tan (7 x)

= \frac{d}{d x} (5 x^{2} + x + 9) tan (7 x) + \frac{d}{d x} (tan (7 x)) (5 x^{2} + x + 9)

\frac{d}{d x} (5 x^{2} + x + 9) = 10 x + 1

\frac{d}{d x} (tan (7 x)) = sec^{2} (7 x) \cdot 7

= (10 x + 1) tan (7 x) + sec^{2} (7 x) \cdot 7 (5 x^{2} + x + 9)