derivative y=x(3x+4)^5

Lösung

ableitung von

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

(3 x + 4)^{5} + 15 x (3 x + 4)^{4}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = (3 x + 4)^{5}

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

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

\frac{d}{d x} ((3 x + 4)^{5}) = 15 (3 x + 4)^{4}

= 1 \cdot (3 x + 4)^{5} + 15 (3 x + 4)^{4} x

Vereinfache

= (3 x + 4)^{5} + 15 x (3 x + 4)^{4}

d er i v a t i v e y = \frac{1}{( x + 1 ) ^{2}}

\frac{\partial}{\partial x} (\frac{9 x z}{x + y})

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\int_{0}^{3} (9 - x^{2}) d x

\frac{\partial}{\partial x} (3 x y^{2} + 9 x)