(\partial)/(\partial x)(ln(5x^2+4y^2+9))

Lösung

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 9))

\frac{10 x}{5 x ^{2} + 4 y ^{2} + 9}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 9))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{5 x ^{2} + 4 y ^{2} + 9} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 9)

= \frac{1}{5 x ^{2} + 4 y ^{2} + 9} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 9)

\frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 9) = 10 x

= \frac{1}{5 x ^{2} + 4 y ^{2} + 9} \cdot 10 x

Vereinfache

\frac{1}{5 x ^{2} + 4 y ^{2} + 9} \cdot 10 x : \frac{10 x}{5 x ^{2} + 4 y ^{2} + 9}

= \frac{10 x}{5 x ^{2} + 4 y ^{2} + 9}

\int \frac{12 x ^{3}}{2 - x ^{4}} d x

d er i v a t i v e f (x) = 5 x^{4} + \frac{1}{( 2 x ^{2} )}

\int_{- 3}^{3} x^{2} + y^{2} d y

x \to 4 lim (3 x - 7)

d er i v a t i v e sin (x) + csc (x)