derivative of (x^2+sin(x)sec(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial t} (s + t)

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 sin (2 t)

- 2 x^{2} y^{^{''}} + 3 x y^{^{'}} - y = 0

\int \frac{x ^{4}}{x ^{2} + 3} d x

\frac{d}{d x} ((x + c) e^{- x})