derivative of (xy^3+x^2y^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

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

\int \frac{1}{9 x + 7} d x

\frac{d}{d x} (\frac{1}{3 ( x - 1 ) ^{\frac{2}{3}}})

\int (\frac{9}{x} - \frac{4}{x ^{3}}) d x

\frac{d}{d θ} (cos (θ) - sin (θ))

im pl i c i t \frac{d y}{d x}, y^{3} = x^{4}