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人気のある微分積分 >

(\partial)/(\partial x)((3x+4y)^5)

解

\frac{\partial}{\partial x} ((3 x + 4 y)^{5})

解

15 (3 x + 4 y)^{4}

解答ステップ

\frac{\partial}{\partial x} ((3 x + 4 y)^{5})

y

を定数として扱う

連鎖法則を適用:

5 (3 x + 4 y)^{4} \frac{\partial}{\partial x} (3 x + 4 y)

= 5 (3 x + 4 y)^{4} \frac{\partial}{\partial x} (3 x + 4 y)

\frac{\partial}{\partial x} (3 x + 4 y) = 3

= 5 (3 x + 4 y)^{4} \cdot 3

簡素化

= 15 (3 x + 4 y)^{4}

人気の例

derivative y=(x^5)/(1-x^4)

d er i v a t i v e y = \frac{x ^{5}}{1 - x ^{4}}

limit as x approaches infinity of sin(0)

x \to \infty lim (sin (0))

sum from n=2 to infinity of (ln(n))/(7n)

n = 2 \sum \infty \frac{ln ( n )}{7 n}

sum from n=0 to infinity of (2n)/(n^2+1)

n = 0 \sum \infty \frac{2 n}{n ^{2} + 1}

derivative x/(x^2+4)

d er i v a t i v e \frac{x}{x ^{2} + 4}