derivative ((2x^2tan(x)))/(sec(x))

Lösung

ableitung von

\frac{( 2 x ^{2} tan ( x ) )}{sec ( x )}

2 (x^{2} cos (x) + 2 x sin (x))

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = tan (x) cos (x)

= 2 (\frac{d}{d x} (x^{2}) tan (x) cos (x) + \frac{d}{d x} (tan (x) cos (x)) x^{2})

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

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

= 2 (2 x tan (x) cos (x) + cos (x) x^{2})

cos (x) tan (x) = sin (x)

= 2 (x^{2} cos (x) + 2 x sin (x))

x \to 0 lim (e^{x} cos (2 x))

\int_{2}^{e^{3}} \frac{1}{x} d x

d er i v a t i v e y = \frac{2 cos ( x )}{x + 1}

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

in v erse l a pl a ce \frac{- s}{7 s ^{2} + 26 s + 25}