(\partial)/(\partial x)(4xy^8+x^3y^2)

Lösung

\frac{\partial}{\partial x} (4 x y^{8} + x^{3} y^{2})

4 y^{8} + 3 y^{2} x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x y^{8} + x^{3} y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 x y^{8}) + \frac{\partial}{\partial x} (x^{3} y^{2})

\frac{\partial}{\partial x} (4 x y^{8}) = 4 y^{8}

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

= 4 y^{8} + 3 y^{2} x^{2}

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

\int \frac{1}{4 + x ^{2}} d x

d er i v a t i v e f (x) = 2 x ln (3 x) - 2 x

\int (x - 1)^{2} x^{3} (2 - x) d x

x \to - \infty lim (\frac{4}{x} - 12)