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

Lösung

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

2 x sec (x) + sec (x) tan (x) x^{2}

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

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

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

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

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

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

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

\int \frac{1}{2} e^{2 x} cos (x) d x

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

d er i v a t i v e q (t) = sin^{2} (\frac{t ^{4}}{t ^{5} - 6 t})

\int_{1}^{4} 1 t ln (t) d t

\frac{d x}{d t} = \frac{1}{x e ^{t + 3 x}}