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Beliebt Rechnen >

derivative of 25(x^2-y^2)

Lösung

\frac{d}{d x} (25 (x^{2} - y^{2}))

Lösung

25 (2 x - 2 y \frac{d y}{d x})

Schritte zur Lösung

\frac{d}{d x} (25 (x^{2} - y^{2}))

Entferne die Konstante:

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

= 25 \frac{d}{d x} (x^{2} - y^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 25 (\frac{d}{d x} (x^{2}) - \frac{d}{d x} (y^{2}))

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

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

= 25 (2 x - 2 y \frac{d y}{d x})

Beliebte Beispiele

derivative of (10^x/(10^x+4))

\frac{d}{d x} (\frac{1 0 ^{x}}{1 0 ^{x} + 4})

derivative of e^{-6x^2}

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

integral of e^{-x}(1-x)

\int e^{- x} (1 - x) d x

(\partial)/(\partial x)(x/(x^7-y^6))

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

integral of (x^2-5)^5(2x)

\int (x^{2} - 5)^{5} (2 x) d x