(\partial)/(\partial x)(5xy^4+2ycos(x))

Lösung

\frac{\partial}{\partial x} (5 x y^{4} + 2 y cos (x))

5 y^{4} - 2 y sin (x)

Schritte zur Lösung

\frac{\partial}{\partial x} (5 x y^{4} + 2 y cos (x))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (5 x y^{4}) + \frac{\partial}{\partial x} (2 y cos (x))

\frac{\partial}{\partial x} (5 x y^{4}) = 5 y^{4}

\frac{\partial}{\partial x} (2 y cos (x)) = - 2 y sin (x)

= 5 y^{4} - 2 y sin (x)

d er i v a t i v e y = x^{3} e^{4 x}

\int \frac{e ^{- 2 x} + e ^{2 x}}{2} d x

t an g e n t f (x) = \frac{18}{( 2 x + 4 ) ^{2}}, at x = 9

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

\frac{\partial}{\partial x} (5^{x y})