derivative f(x)=e^{xsqrt(7x+6)}

解

導関数

f (x) = e^{x 7 x + 6}

\frac{e ^{x 7 x + 6} ( 21 x + 12 )}{2 7 x + 6}

解答ステップ

\frac{d}{d x} (e^{x 7 x + 6})

連鎖法則を適用:

e^{x 7 x + 6} \frac{d}{d x} (x 7 x + 6)

= e^{x 7 x + 6} \frac{d}{d x} (x 7 x + 6)

\frac{d}{d x} (x 7 x + 6) = \frac{21 x + 12}{2 7 x + 6}

= e^{x 7 x + 6} \frac{21 x + 12}{2 7 x + 6}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{x 7 x + 6} ( 21 x + 12 )}{2 7 x + 6}