derivative of (2x^3-5(x^2-5ln(x)))

Lösung

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

10 x^{4} - 30 x^{2} ln (x) - 10 x^{2} - 10 x + \frac{25}{x}

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 x^{3} - 5, g = x^{2} - 5 ln (x)

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

\frac{d}{d x} (2 x^{3} - 5) = 6 x^{2}

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

= 6 x^{2} (x^{2} - 5 ln (x)) + (2 x - \frac{5}{x}) (2 x^{3} - 5)

Vereinfache

6 x^{2} (x^{2} - 5 ln (x)) + (2 x - \frac{5}{x}) (2 x^{3} - 5) : 10 x^{4} - 30 x^{2} ln (x) - 10 x^{2} - 10 x + \frac{25}{x}

= 10 x^{4} - 30 x^{2} ln (x) - 10 x^{2} - 10 x + \frac{25}{x}

\frac{d}{d x} (\frac{x}{csc ( x )})

\frac{\partial}{\partial z} (x^{2} - x yz)

y^{^{''}} - y^{^{'}} - 42 y = 0

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

\int x sin (- 1 x) d x