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人気のある微分積分 >

derivative f(x)=(6x^2+7x)^4

解

導関数

f (x) = (6 x^{2} + 7 x)^{4}

解

4 (6 x^{2} + 7 x)^{3} (12 x + 7)

解答ステップ

\frac{d}{d x} ((6 x^{2} + 7 x)^{4})

連鎖法則を適用:

4 (6 x^{2} + 7 x)^{3} \frac{d}{d x} (6 x^{2} + 7 x)

= 4 (6 x^{2} + 7 x)^{3} \frac{d}{d x} (6 x^{2} + 7 x)

\frac{d}{d x} (6 x^{2} + 7 x) = 12 x + 7

= 4 (6 x^{2} + 7 x)^{3} (12 x + 7)

グラフ

人気の例

derivative y=(x^3+3)^4

d er i v a t i v e y = (x^{3} + 3)^{4}

derivative 1/((x+2)^2)

d er i v a t i v e \frac{1}{( x + 2 ) ^{2}}

derivative of-(cos^2(x+cos^2(y))2)

\frac{d}{d x} (- (cos^{2} (x) + cos^{2} (y)) 2)

derivative 2/(x^{-5)}

d er i v a t i v e \frac{2}{x ^{- 5}}

derivative e^{0.5}t

d er i v a t i v e e^{0.5} t