derivative f(x)=16\sqrt[4]{x}

Lösung

ableitung von

f (x) = 16 4 x

\frac{4}{x ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (16 4 x)

Entferne die Konstante:

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

= 16 \frac{d}{d x} (4 x)

Wende Radikal Regel an:

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

= 16 \frac{d}{d x} (x^{\frac{1}{4}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 16 \cdot \frac{1}{4} x^{\frac{1}{4} - 1}

Vereinfache

16 \cdot \frac{1}{4} x^{\frac{1}{4} - 1} : \frac{4}{x ^{\frac{3}{4}}}

= \frac{4}{x ^{\frac{3}{4}}}

\int \frac{sin ^{7} ( 10 x )}{cos ^{4} ( 10 x )} d x

\frac{\partial}{\partial y} (f (x, y) (x + y))

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x y^{^{'}} - y = - 2 x^{2} - 2 x + 1

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