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Beliebt Rechnen >

derivative y= 1/((4x^2+3)^5)

Lösung

ableitung von

y = \frac{1}{( 4 x ^{2} + 3 ) ^{5}}

Lösung

- \frac{40 x}{( 4 x ^{2} + 3 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( 4 x ^{2} + 3 ) ^{5}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{5}{( 4 x ^{2} + 3 ) ^{6}} \frac{d}{d x} (4 x^{2} + 3)

= - \frac{5}{( 4 x ^{2} + 3 ) ^{6}} \frac{d}{d x} (4 x^{2} + 3)

\frac{d}{d x} (4 x^{2} + 3) = 8 x

= - \frac{5}{( 4 x ^{2} + 3 ) ^{6}} \cdot 8 x

Vereinfache

- \frac{5}{( 4 x ^{2} + 3 ) ^{6}} \cdot 8 x : - \frac{40 x}{( 4 x ^{2} + 3 ) ^{6}}

= - \frac{40 x}{( 4 x ^{2} + 3 ) ^{6}}

Graph

Beliebte Beispiele

integral of (2x^3+5x^2-2x+7)

\int (2 x^{3} + 5 x^{2} - 2 x + 7) d x

(\partial)/(\partial y)(xy+ln(x/y))

\frac{\partial}{\partial y} (x y + ln (\frac{x}{y}))

integral of sqrt(x^4)

\int x^{4} d x

integral of-x^{-2}

\int - x^{- 2} d x

integral of 1/(8+5x)

\int \frac{1}{8 + 5 x} d x