derivative of sqrt(y^2-x)

Lösung

\frac{d}{d x} (y^{2} - x)

\frac{2 y \frac{d y}{d x} - 1}{2 y ^{2} - x}

Schritte zur Lösung

\frac{d}{d x} (y^{2} - x)

Wende die Kettenregel an:

\frac{1}{2 y ^{2} - x} \frac{d}{d x} (y^{2} - x)

= \frac{1}{2 y ^{2} - x} \frac{d}{d x} (y^{2} - x)

\frac{d}{d x} (y^{2} - x) = 2 y \frac{d y}{d x} - 1

= \frac{1}{2 y ^{2} - x} (2 y \frac{d y}{d x} - 1)

Vereinfache

\frac{1}{2 y ^{2} - x} (2 y \frac{d y}{d x} - 1) : \frac{2 y \frac{d y}{d x} - 1}{2 y ^{2} - x}

= \frac{2 y \frac{d y}{d x} - 1}{2 y ^{2} - x}

s im pl i f y e^{l n (s i n (x^{2}))} 2 x + 1

x \to 0 lim (\frac{ln ( x + 1 )}{x})

\int cos^{2} (10 x) d x

\frac{d}{d x} ((x^{4} + 2)^{c o s (x)})

y^{^{''}} + 9 y = 2 sec (3 t)