(\partial)/(\partial x)(xln(z^7+x^3))

解

\frac{\partial}{\partial x} (x ln (z^{7} + x^{3}))

ln (z^{7} + x^{3}) + \frac{3 x ^{3}}{z ^{7} + x ^{3}}

解答ステップ

\frac{\partial}{\partial x} (x ln (z^{7} + x^{3}))

z

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (z^{7} + x^{3})

= \frac{\partial}{\partial x} (x) ln (z^{7} + x^{3}) + \frac{\partial}{\partial x} (ln (z^{7} + x^{3})) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (ln (z^{7} + x^{3})) = \frac{3 x ^{2}}{z ^{7} + x ^{3}}

= 1 \cdot ln (z^{7} + x^{3}) + \frac{3 x ^{2}}{z ^{7} + x ^{3}} x

簡素化

1 \cdot ln (z^{7} + x^{3}) + \frac{3 x ^{2}}{z ^{7} + x ^{3}} x : ln (z^{7} + x^{3}) + \frac{3 x ^{3}}{z ^{7} + x ^{3}}

= ln (z^{7} + x^{3}) + \frac{3 x ^{3}}{z ^{7} + x ^{3}}