derivative of 4sin^5(sqrt(x))

Lösung

\frac{d}{d x} (4 sin^{5} (x))

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

Schritte zur Lösung

\frac{d}{d x} (4 sin^{5} (x))

Entferne die Konstante:

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

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

Wende die Kettenregel an:

5 (sin (x))^{4} \frac{d}{d x} (sin (x))

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

\frac{d}{d x} (sin (x)) = \frac{cos ( x )}{2 x}

= 4 \cdot 5 (sin (x))^{4} \frac{cos ( x )}{2 x}

Vereinfache

4 \cdot 5 sin^{4} (x) \frac{cos ( x )}{2 x} : \frac{10 sin ^{4} ( x ) cos ( x )}{x}

= \frac{10 sin ^{4} ( x ) cos ( x )}{x}

\int (1 + \frac{1}{2 x}) d x

t an g e n t \frac{x}{1 + x ^{2}}

\frac{\partial}{\partial y} (sin (x^{2} + x y))

y^{^{''}} - y = 18 t

\frac{d}{d x} (- x^{2} + 6 x)