(\partial)/(\partial y)(y^x-ln(x^4y+7x))

Lösung

\frac{\partial}{\partial y} (y^{x} - ln (x^{4} y + 7 x))

x y^{x - 1} - \frac{x ^{3}}{x ^{3} y + 7}

Schritte zur Lösung

\frac{\partial}{\partial y} (y^{x} - ln (x^{4} y + 7 x))

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (y^{x}) - \frac{\partial}{\partial y} (ln (x^{4} y + 7 x))

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

\frac{\partial}{\partial y} (ln (x^{4} y + 7 x)) = \frac{x ^{3}}{x ^{3} y + 7}

= x y^{x - 1} - \frac{x ^{3}}{x ^{3} y + 7}

\int \frac{6 x}{1 - 7 x ^{2}} d x

2 x y^{^{'}} + y = 10 x

\int (x^{3} + 1)^{3} d x

t an g e n t f (x) = x^{2} - 2 x + 1

x \to \infty lim ((x)^{2})