(\partial)/(\partial x)(5sqrt(9x^2+16y^2))

解

\frac{\partial}{\partial x} (5 9 x^{2} + 16 y^{2})

\frac{45 x}{9 x ^{2} + 16 y ^{2}}

解答ステップ

\frac{\partial}{\partial x} (5 9 x^{2} + 16 y^{2})

y

を定数として扱う

定数を除去:

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

= 5 \frac{\partial}{\partial x} (9 x^{2} + 16 y^{2})

連鎖法則を適用:

\frac{1}{2 9 x ^{2} + 16 y ^{2}} \frac{\partial}{\partial x} (9 x^{2} + 16 y^{2})

= \frac{1}{2 9 x ^{2} + 16 y ^{2}} \frac{\partial}{\partial x} (9 x^{2} + 16 y^{2})

\frac{\partial}{\partial x} (9 x^{2} + 16 y^{2}) = 18 x

= 5 \cdot \frac{1}{2 9 x ^{2} + 16 y ^{2}} \cdot 18 x

簡素化

5 \cdot \frac{1}{2 9 x ^{2} + 16 y ^{2}} \cdot 18 x : \frac{45 x}{9 x ^{2} + 16 y ^{2}}

= \frac{45 x}{9 x ^{2} + 16 y ^{2}}