derivative (8x^2-5)^{1/2}

Lösung

ableitung von

(8 x^{2} - 5)^{\frac{1}{2}}

\frac{8 x}{( 8 x ^{2} - 5 ) ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} ((8 x^{2} - 5)^{\frac{1}{2}})

Wende die Kettenregel an:

\frac{1}{2 ( 8 x ^{2} - 5 ) ^{\frac{1}{2}}} \frac{d}{d x} (8 x^{2} - 5)

= \frac{1}{2 ( 8 x ^{2} - 5 ) ^{\frac{1}{2}}} \frac{d}{d x} (8 x^{2} - 5)

\frac{d}{d x} (8 x^{2} - 5) = 16 x

= \frac{1}{2 ( 8 x ^{2} - 5 ) ^{\frac{1}{2}}} \cdot 16 x

Vereinfache

\frac{1}{2 ( 8 x ^{2} - 5 ) ^{\frac{1}{2}}} \cdot 16 x : \frac{8 x}{( 8 x ^{2} - 5 ) ^{\frac{1}{2}}}

= \frac{8 x}{( 8 x ^{2} - 5 ) ^{\frac{1}{2}}}

\int_{0}^{3} (2 x - 1) d x

d er i v a t i v e f (y) = 5 x + \frac{135}{x} (15 x + 30)

\int \frac{4 e ^{x}}{e ^{x} + 3} d x

f (x) = (e^{x} + 1)^{7 x}

y^{^{'''}} + 8 y^{^{''}} - 12 y^{^{'}} - 144 y = 0