(\partial)/(\partial x)(3sqrt(xy^2+9x))

解

\frac{\partial}{\partial x} (3 x y^{2} + 9 x)

\frac{3 ( y ^{2} + 9 )}{2 x y ^{2} + 9 x}

解答ステップ

\frac{\partial}{\partial x} (3 x y^{2} + 9 x)

y

を定数として扱う

定数を除去:

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

= 3 \frac{\partial}{\partial x} (x y^{2} + 9 x)

連鎖法則を適用:

\frac{1}{2 x y ^{2} + 9 x} \frac{\partial}{\partial x} (x y^{2} + 9 x)

= \frac{1}{2 x y ^{2} + 9 x} \frac{\partial}{\partial x} (x y^{2} + 9 x)

\frac{\partial}{\partial x} (x y^{2} + 9 x) = y^{2} + 9

= 3 \cdot \frac{1}{2 x y ^{2} + 9 x} (y^{2} + 9)

簡素化

3 \cdot \frac{1}{2 x y ^{2} + 9 x} (y^{2} + 9) : \frac{3 ( y ^{2} + 9 )}{2 x y ^{2} + 9 x}

= \frac{3 ( y ^{2} + 9 )}{2 x y ^{2} + 9 x}