derivative of ln(7x^2+5y^2)

Lösung

\frac{d}{d x} (ln (7 x^{2} + 5 y^{2}))

\frac{14 x + 10 y \frac{d y}{d x}}{7 x ^{2} + 5 y ^{2}}

Schritte zur Lösung

\frac{d}{d x} (ln (7 x^{2} + 5 y^{2}))

Wende die Kettenregel an:

\frac{1}{7 x ^{2} + 5 y ^{2}} \frac{d}{d x} (7 x^{2} + 5 y^{2})

= \frac{1}{7 x ^{2} + 5 y ^{2}} \frac{d}{d x} (7 x^{2} + 5 y^{2})

\frac{d}{d x} (7 x^{2} + 5 y^{2}) = 14 x + 10 y \frac{d y}{d x}

= \frac{1}{7 x ^{2} + 5 y ^{2}} (14 x + 10 y \frac{d y}{d x})

Vereinfache

\frac{1}{7 x ^{2} + 5 y ^{2}} (14 x + 10 y \frac{d y}{d x}) : \frac{14 x + 10 y \frac{d y}{d x}}{7 x ^{2} + 5 y ^{2}}

= \frac{14 x + 10 y \frac{d y}{d x}}{7 x ^{2} + 5 y ^{2}}

d er i v a t i v e 4 t^{\frac{- 1}{8}} + 5 ln (t) + ln (5)

t an g e n t f (x) = 3 x^{2} - 4 x + 1

\frac{d}{d x} (\frac{9 - sec ( x )}{tan ( x )})

\int (x^{3} + 5) d x

\int e^{\frac{t}{5}} d t