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Beliebt Rechnen >

(\partial)/(\partial x)(sqrt(4x^2+3y^2))

Lösung

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

Lösung

\frac{4 x}{4 x ^{2} + 3 y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 4 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

= \frac{1}{2 4 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2}) = 8 x

= \frac{1}{2 4 x ^{2} + 3 y ^{2}} \cdot 8 x

Vereinfache

\frac{1}{2 4 x ^{2} + 3 y ^{2}} \cdot 8 x : \frac{4 x}{4 x ^{2} + 3 y ^{2}}

= \frac{4 x}{4 x ^{2} + 3 y ^{2}}

Beliebte Beispiele

derivative of log_{3}(\sqrt[5]{x+2})

\frac{d}{d x} (lo g_{3} (5 x + 2))

y^2*((dy)/(dx))+y^3=1

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

integral of (x^3+1)/(x^2+5x+6)

\int \frac{x ^{3} + 1}{x ^{2} + 5 x + 6} d x

derivative of 1/(2x^2+4)

\frac{d}{d x} (\frac{1}{2 x ^{2} + 4})

derivative of 750+12x-0.08x^7

\frac{d}{d x} (750 + 12 x - 0.08 x^{7})