derivative [3(3x^5+6)^3](12x^3)

해법

유도체

[3 (3 x^{5} + 6)^{3}] (12 x^{3})

36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{7} (3 x^{5} + 6)^{2})

솔루션 단계

\frac{d}{d x} ((3 (3 x^{5} + 6)^{3}) \cdot 12 x^{3})

(3 (3 x^{5} + 6)^{3}) \cdot 12 x^{3}

단순화하세요:

36 x^{3} (3 x^{5} + 6)^{3}

= \frac{d}{d x} (36 x^{3} (3 x^{5} + 6)^{3})

정수를 빼라:

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

= 36 \frac{d}{d x} (x^{3} (3 x^{5} + 6)^{3})

곱 규칙 적용:

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

f = x^{3}, g = (3 x^{5} + 6)^{3}

= 36 (\frac{d}{d x} (x^{3}) (3 x^{5} + 6)^{3} + \frac{d}{d x} ((3 x^{5} + 6)^{3}) x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} ((3 x^{5} + 6)^{3}) = 45 x^{4} (3 x^{5} + 6)^{2}

= 36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{4} (3 x^{5} + 6)^{2} x^{3})

45 x^{4} (3 x^{5} + 6)^{2} x^{3} = 45 x^{7} (3 x^{5} + 6)^{2}

= 36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{7} (3 x^{5} + 6)^{2})