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Beliebt Rechnen >

derivative of 3x^2y^3

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = y^{3}

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

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

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

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

Beliebte Beispiele

derivative of x^2(2x-1^4)

\frac{d}{d x} (x^{2} (2 x - 1)^{4})

derivative of 2^{5x}

\frac{d}{d x} (2^{5 x})

sum from k=1 to infinity of (k^3)/(3^k)

k = 1 \sum \infty \frac{k ^{3}}{3 ^{k}}

y^'+3y=2e^{-3x}

y^{^{'}} + 3 y = 2 e^{- 3 x}

tangent f(x)= 2/x ,\at x=-1

t an g e n t f (x) = \frac{2}{x}, at x = - 1