derivative of 5x^3y^4

Lösung

\frac{d}{d x} (5 x^{3} y^{4})

5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3})

Schritte zur Lösung

\frac{d}{d x} (5 x^{3} y^{4})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x^{3} y^{4})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = y^{4}

= 5 (\frac{d}{d x} (x^{3}) y^{4} + \frac{d}{d x} (y^{4}) x^{3})

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

\frac{d}{d x} (y^{4}) = 4 y^{3} \frac{d y}{d x}

= 5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3})

(\frac{d y}{d x})^{2} + 2 e^{x} \frac{d y}{d x} + e^{2 x} = 0

d er i v a t i v e 11 - x^{2}

\int \frac{x ^{2}}{( 9 - x ^{2} ) ^{\frac{3}{2}}} d x

\int_{1}^{1000} \frac{37}{x ^{3}} d x

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 7 y^{3})