derivative of 0.005x^2-ln(x^{16}+70)

Lösung

\frac{d}{d x} (0.005 x^{2} - ln (x^{16}) + 70)

0.01 x - \frac{16}{x}

Schritte zur Lösung

\frac{d}{d x} (0.005 x^{2} - ln (x^{16}) + 70)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (0.005 x^{2}) - \frac{d}{d x} (ln (x^{16})) + \frac{d}{d x} (70)

\frac{d}{d x} (0.005 x^{2}) = 0.01 x

\frac{d}{d x} (ln (x^{16})) = \frac{16}{x}

\frac{d}{d x} (70) = 0

= 0.01 x - \frac{16}{x} + 0

Vereinfache

= 0.01 x - \frac{16}{x}

d er i v a t i v e y = \frac{6 x ^{2} + 8 x + 2}{x}

d er i v a t i v e - 4 x^{\frac{1}{2}}

s im pl i f y \frac{x}{2} ln (\frac{1 + x}{1 - x}) - 1

\frac{\partial}{\partial x} ((x - 1) y^{2} e^{x y})

\frac{d y}{d x} = \frac{y}{2 x}