derivative of x(2x+1^3)

Lösung

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

(2 x + 1)^{3} + 6 x (2 x + 1)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = (2 x + 1)^{3}

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

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

\frac{d}{d x} ((2 x + 1)^{3}) = 6 (2 x + 1)^{2}

= 1 \cdot (2 x + 1)^{3} + 6 (2 x + 1)^{2} x

Vereinfache

= (2 x + 1)^{3} + 6 x (2 x + 1)^{2}

t an g e n t f (x) = (4 x^{2} - 3 x)^{2}, at x = 1

\int \frac{x ^{2} + 20 x - 4}{x ^{3} - 4 x} d x

\frac{\partial}{\partial z} (x y^{2} e^{- x z})

(12 x^{2} - 20 y^{2}) d x + (- 20 x y + 36 x^{- 1} y^{3}) d y = 0

\int e^{x} d x