derivative (f(5x))^2-2

Lösung

ableitung von

(f (5 x))^{2} - 2

50 f x^{2}

Schritte zur Lösung

\frac{d}{df} ((f \cdot 5 x)^{2} - 2)

Vereinfache

(f \cdot 5 x)^{2} - 2 : 25 f^{2} x^{2} - 2

= \frac{d}{df} (25 f^{2} x^{2} - 2)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{d}{df} (25 f^{2} x^{2}) - \frac{d}{df} (2)

\frac{d}{df} (25 f^{2} x^{2}) = 50 x^{2} f

\frac{d}{df} (2) = 0

= 50 x^{2} f - 0

Vereinfache

= 50 f x^{2}

\int \frac{sec ^{2} ( \frac{1}{x ^{5}} )}{x ^{6}} d x

\int \frac{1}{( 16 + x ^{2} ) ^{\frac{3}{2}}} d x

roo t s a x + b

\int_{1}^{4} x^{2} - 3 x + 12 d x

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