derivative of (sec(4x+tan(2x))^5)

الحلّ

\frac{d}{d x} ((sec (4 x) + tan (2 x))^{5})

5 (sec (4 x) + tan (2 x))^{4} (sec (4 x) tan (4 x) \cdot 4 + sec^{2} (2 x) \cdot 2)

خطوات الحلّ

\frac{d}{d x} ((sec (4 x) + tan (2 x))^{5})

استعمل قانون السلسلة:

5 (sec (4 x) + tan (2 x))^{4} \frac{d}{d x} (sec (4 x) + tan (2 x))

= 5 (sec (4 x) + tan (2 x))^{4} \frac{d}{d x} (sec (4 x) + tan (2 x))

\frac{d}{d x} (sec (4 x) + tan (2 x)) = sec (4 x) tan (4 x) \cdot 4 + sec^{2} (2 x) \cdot 2

= 5 (sec (4 x) + tan (2 x))^{4} (sec (4 x) tan (4 x) \cdot 4 + sec^{2} (2 x) \cdot 2)

\frac{d}{d x} ((x^{2} + 3 x) (x - 2) (x^{2} + 1))

y = 2 x - x^{2}, (0, 2)

9 sin (3 x)

\int_{0}^{1} - x + 2 d x

f (x) = lo g_{3} (4 x^{2} + 2 x)