derivative of (3(-x^2+2\sqrt[5]{x^2}))

Lösung

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

\frac{3 ( 4 - 10 x ^{\frac{8}{5}} )}{5 x ^{\frac{3}{5}}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Vereinfache

3 (- 2 x + \frac{4}{5 x ^{\frac{3}{5}}}) : \frac{3 ( 4 - 10 x ^{\frac{8}{5}} )}{5 x ^{\frac{3}{5}}}

= \frac{3 ( 4 - 10 x ^{\frac{8}{5}} )}{5 x ^{\frac{3}{5}}}

e x p an d \frac{x ^{4} + y ^{4}}{x y ( y ^{2} + x ^{2} )}

e x p an d \frac{2 x + 1}{x ^{2} ( x + 1 ) ^{2}}

s im pl i f y \frac{e ^{(- 2 + i) t} + e ^{(- 2 - i) t}}{2}

e x p an d \frac{( 2 + s ^{5} - s ^{4} + 2 s ^{3} )}{s ^{4} ( s ^{2} - s + 2 )}

e x p an d \frac{x ( 4 - x )}{2}