derivative of 3xsqrt(y)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = y

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{2 x}{( x ^{2} + 4 ) ^{2}}

\frac{d}{d x} (ln (arctan (8 x^{5})))

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

\int 3 x \cdot (x + 1)^{2} d x

(1 + y^{2} + x y^{2}) d x + (x^{2} y + y + 2 x y) d y = 0