derivative of (sin(x)/(cos(x^2)))

Lösung

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

cos (x) sec (x^{2}) + sec (x^{2}) tan (x^{2}) \cdot 2 x sin (x)

Schritte zur Lösung

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

Vereinfache

\frac{sin ( x )}{cos ( x ^{2} )} : sin (x) sec (x^{2})

= \frac{d}{d x} (sin (x) sec (x^{2}))

Wende die Produktregel an:

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

f = sin (x), g = sec (x^{2})

= \frac{d}{d x} (sin (x)) sec (x^{2}) + \frac{d}{d x} (sec (x^{2})) sin (x)

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

\frac{d}{d x} (sec (x^{2})) = sec (x^{2}) tan (x^{2}) \cdot 2 x

= cos (x) sec (x^{2}) + sec (x^{2}) tan (x^{2}) \cdot 2 x sin (x)

\int x^{4} \cdot e^{- 6 x^{5}} d x

\frac{d}{d x} (8 sin^{3} (x))

\int (8 x + 4) e^{(x^{2} + x)} d x

d er i v a t i v e f (x) = x^{2} - tan (x)

\int_{0}^{1} \frac{x}{x ^{2} + 4 x + 4} d x