derivative ((sqrt(x))/7+1)^{3/2}

Lösung

ableitung von

(\frac{x}{7} + 1)^{\frac{3}{2}}

\frac{3 ( x + 7 ) ^{\frac{1}{2}}}{28 \cdot 7 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x}{7} + 1)^{\frac{3}{2}})

Vereinfache

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

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

Wende die Kettenregel an:

\frac{3 ( \frac{x + 7}{7} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x + 7}{7})

= \frac{3 ( \frac{x + 7}{7} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x + 7}{7})

\frac{d}{d x} (\frac{x + 7}{7}) = \frac{1}{14 x ^{\frac{1}{2}}}

= \frac{3 ( \frac{x + 7}{7} ) ^{\frac{1}{2}}}{2} \cdot \frac{1}{14 x ^{\frac{1}{2}}}

Vereinfache

\frac{3 ( \frac{x + 7}{7} ) ^{\frac{1}{2}}}{2} \cdot \frac{1}{14 x ^{\frac{1}{2}}} : \frac{3 ( x + 7 ) ^{\frac{1}{2}}}{28 \cdot 7 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

= \frac{3 ( x + 7 ) ^{\frac{1}{2}}}{28 \cdot 7 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

\int_{1}^{3} x^{2} + \frac{1}{4 x ^{2}} d x

d er i v a t i v e 3 x + π^{2}

a re a y = 4 x, x = 5, y = \frac{4}{x}

\int (y + 1) x^{2} sin (\frac{x y}{2}) d y

d er i v a t i v e 1 - t^{2}