(\partial)/(\partial x)(1/(2cos^2(x)))

Lösung

\frac{\partial}{\partial x} (\frac{1}{2 cos ^{2} ( x )})

sec^{3} (x) sin (x)

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{2 cos ^{2} ( x )})

Entferne die Konstante:

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

= \frac{1}{2} \frac{\partial}{\partial x} (\frac{1}{cos ^{2} ( x )})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{1}{2} \frac{\partial}{\partial x} (cos^{- 2} (x))

Wende die Kettenregel an:

- \frac{2}{( cos ( x ) ) ^{3}} \frac{\partial}{\partial x} (cos (x))

= - \frac{2}{( cos ( x ) ) ^{3}} \frac{\partial}{\partial x} (cos (x))

\frac{\partial}{\partial x} (cos (x)) = - sin (x)

= \frac{1}{2} (- \frac{2}{( cos ( x ) ) ^{3}} (- sin (x)))

Vereinfache

\frac{1}{2} (- \frac{2}{cos ^{3} ( x )} (- sin (x))) : sec^{3} (x) sin (x)

= sec^{3} (x) sin (x)

\int 3 x^{2} + x d x

x \to 10 - lim (\frac{1}{( x - 10 ) ^{2}})

d er i v a t i v e f (x) = e^{θ} sin (6 θ)

x \to 2 lim (3 x^{2} - x + 5)

\frac{\partial}{\partial x} (- 5 x^{2} - 5 y^{2} + x y)