derivative of 3sqrt(x^2+y^2)

Lösung

\frac{d}{d x} (3 x^{2} + y^{2})

\frac{3 ( x + y \frac{d y}{d x} )}{x ^{2} + y ^{2}}

Schritte zur Lösung

\frac{d}{d x} (3 x^{2} + y^{2})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= 3 \cdot \frac{1}{2 x ^{2} + y ^{2}} (2 x + 2 y \frac{d y}{d x})

Vereinfache

3 \cdot \frac{1}{2 x ^{2} + y ^{2}} (2 x + 2 y \frac{d y}{d x}) : \frac{3 ( x + y \frac{d y}{d x} )}{x ^{2} + y ^{2}}

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

\frac{\partial}{\partial x} (- 7 x^{2} e^{6 x})

a re a x = 3 y^{2}, x = 0, [0, 2]

\int \frac{5 x ^{4} + 6}{( x ^{5} + 6 x ) ^{2}} d x

\frac{d y}{d x} = x^{2} + x

\frac{d}{d x} (x^{4} sin (x))