derivative of 5sqrt(x)cos(x/5)

Lösung

\frac{d}{d x} (5 x cos (\frac{x}{5}))

\frac{5 cos ( \frac{x}{5} )}{2 x} - x sin (\frac{x}{5})

Schritte zur Lösung

\frac{d}{d x} (5 x cos (\frac{x}{5}))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x cos (\frac{x}{5}))

Wende die Produktregel an:

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

f = x, g = cos (\frac{x}{5})

= 5 (\frac{d}{d x} (x) cos (\frac{x}{5}) + \frac{d}{d x} (cos (\frac{x}{5})) x)

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (cos (\frac{x}{5})) = - sin (\frac{x}{5}) \frac{1}{5}

= 5 (\frac{1}{2 x} cos (\frac{x}{5}) + (- sin (\frac{x}{5}) \frac{1}{5}) x)

Vereinfache

5 (\frac{1}{2 x} cos (\frac{x}{5}) + (- sin (\frac{x}{5}) \frac{1}{5}) x) : \frac{5 cos ( \frac{x}{5} )}{2 x} - x sin (\frac{x}{5})

= \frac{5 cos ( \frac{x}{5} )}{2 x} - x sin (\frac{x}{5})

\int_{6}^{7} \frac{x}{x ^{2} + 6 x + 13} d x

y^{^{''}} + \frac{1}{2} y^{^{'}} + y = 0

d er i v a t i v e x^{2} + 3 x - 4

t an g e n t x^{2} - 3 x

x \to 0 lim ((1 + 8 x)^{\frac{7}{x}})