(\partial)/(\partial y)(e^xsec^2(y))

Lösung

\frac{\partial}{\partial y} (e^{x} sec^{2} (y))

2 e^{x} sec^{2} (y) tan (y)

Schritte zur Lösung

\frac{\partial}{\partial y} (e^{x} sec^{2} (y))

Behandle

x

als Konstante

Entferne die Konstante:

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

= e^{x} \frac{\partial}{\partial y} (sec^{2} (y))

Wende die Kettenregel an:

2 sec (y) \frac{\partial}{\partial y} (sec (y))

= 2 sec (y) \frac{\partial}{\partial y} (sec (y))

\frac{\partial}{\partial y} (sec (y)) = sec (y) tan (y)

= e^{x} \cdot 2 sec (y) sec (y) tan (y)

Vereinfache

e^{x} \cdot 2 sec (y) sec (y) tan (y) : 2 e^{x} sec^{2} (y) tan (y)

= 2 e^{x} sec^{2} (y) tan (y)

t an g e n t f (x) = x^{2} - 8, (4, 8)

t an g e n t y = 9 x - 6 x, (1, 3)

\int_{0}^{1} \frac{ln ( x )}{x ^{2}} d x

\int sin (x^{2}) + cos (2 x) - \frac{1}{2} d x

\int_{0}^{2} \frac{x}{x ^{2} + 6 x + 13} d x