derivative of 4x^3y^3

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

d er i v a t i v e f (x) = 4 x + 32

a re a f (x) = ((25 - x^{2})^{\frac{1}{2}}), \frac{4}{3} x, 5

\frac{\partial}{\partial x} (a e^{2 x})

\int \frac{1}{( a + b x ) ^{2}} d x

\int \frac{1}{16 x ^{4} - 1} d x