derivative of 1/((3x^3+5x+7^{3/4)})

Lösung

\frac{d}{d x} (\frac{1}{( 3 x ^{3} + 5 x + 7 ) ^{\frac{3}{4}}})

- \frac{3 ( 9 x ^{2} + 5 )}{4 ( 3 x ^{3} + 5 x + 7 ) ^{\frac{7}{4}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( 3 x ^{3} + 5 x + 7 ) ^{\frac{3}{4}}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((3 x^{3} + 5 x + 7)^{- \frac{3}{4}})

Wende die Kettenregel an:

- \frac{3}{4 ( 3 x ^{3} + 5 x + 7 ) ^{\frac{7}{4}}} \frac{d}{d x} (3 x^{3} + 5 x + 7)

= - \frac{3}{4 ( 3 x ^{3} + 5 x + 7 ) ^{\frac{7}{4}}} \frac{d}{d x} (3 x^{3} + 5 x + 7)

\frac{d}{d x} (3 x^{3} + 5 x + 7) = 9 x^{2} + 5

= - \frac{3}{4 ( 3 x ^{3} + 5 x + 7 ) ^{\frac{7}{4}}} (9 x^{2} + 5)

Multipliziere Brüche:

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

= - \frac{3 ( 9 x ^{2} + 5 )}{4 ( 3 x ^{3} + 5 x + 7 ) ^{\frac{7}{4}}}

x \to 16 lim (4 - x)

d er i v a t i v e f (x) = (2 x^{5} - 3)^{8}

x \to + (- 2.4) lim (x)

n = 7 \sum \infty \frac{1}{n}

x \to - 5 lim (\frac{x - 1}{x + 5})