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人気のある微分積分 >

derivative 6(2x^3+3)6x^2

解

導関数

6 (2 x^{3} + 3) 6 x^{2}

解

36 (10 x^{4} + 6 x)

解答ステップ

\frac{d}{d x} (6 (2 x^{3} + 3) \cdot 6 x^{2})

簡素化

6 (2 x^{3} + 3) \cdot 6 x^{2} : 36 x^{2} (2 x^{3} + 3)

= \frac{d}{d x} (36 x^{2} (2 x^{3} + 3))

定数を除去:

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

= 36 \frac{d}{d x} (x^{2} (2 x^{3} + 3))

積の法則を適用:

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

f = x^{2}, g = 2 x^{3} + 3

= 36 (\frac{d}{d x} (x^{2}) (2 x^{3} + 3) + \frac{d}{d x} (2 x^{3} + 3) x^{2})

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

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

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

簡素化

36 (2 x (2 x^{3} + 3) + 6 x^{2} x^{2}) : 36 (10 x^{4} + 6 x)

= 36 (10 x^{4} + 6 x)

グラフ

人気の例

integral of (2-4x^2)/(x-x^3)

\int \frac{2 - 4 x ^{2}}{x - x ^{3}} d x

tangent y=F-x^2-x,\at x=-2

t an g e n t y = F - x^{2} - x, at x = - 2

derivative f(x)=10sqrt(t)

d er i v a t i v e f (x) = 10 t

y^{^{'}} = x + 4 y

sum from n=0 to infinity of 2n

n = 0 \sum \infty 2 n