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人気のある微分積分 >

derivative f(x)=sqrt(x^2+5x)

解

導関数

f (x) = x^{2} + 5 x

解

\frac{2 x + 5}{2 x ^{2} + 5 x}

解答ステップ

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

連鎖法則を適用:

\frac{1}{2 x ^{2} + 5 x} \frac{d}{d x} (x^{2} + 5 x)

= \frac{1}{2 x ^{2} + 5 x} \frac{d}{d x} (x^{2} + 5 x)

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

= \frac{1}{2 x ^{2} + 5 x} (2 x + 5)

簡素化

\frac{1}{2 x ^{2} + 5 x} (2 x + 5) : \frac{2 x + 5}{2 x ^{2} + 5 x}

= \frac{2 x + 5}{2 x ^{2} + 5 x}

グラフ

人気の例

derivative of e^{sqrt(ln(x^2+1+x)})

\frac{d}{d x} (e^{l n (x^{2} + 1) + x})

integral from-1 to 6 of (9y)/(y^2-5y-14)

\int_{- 1}^{6} \frac{9 y}{y ^{2} - 5 y - 14} d y

integral from 1 to 2 of (4/x-(16)/(x^2))

\int_{1}^{2} (\frac{4}{x} - \frac{16}{x ^{2}}) d x

y^{^{'}} - 2 t y = t

integral of (5cos^2(x))/(sin(x))

\int \frac{5 cos ^{2} ( x )}{sin ( x )} d x