derivative f(x)=(2x^2-1)^2(3x^2)

Lösung

ableitung von

f (x) = (2 x^{2} - 1)^{2} (3 x^{2})

3 (24 x^{5} - 16 x^{3} + 2 x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} ((2 x^{2} - 1)^{2}) = 8 x (2 x^{2} - 1)

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

= 3 (8 x (2 x^{2} - 1) x^{2} + 2 x (2 x^{2} - 1)^{2})

Vereinfache

3 (8 x (2 x^{2} - 1) x^{2} + 2 x (2 x^{2} - 1)^{2}) : 3 (24 x^{5} - 16 x^{3} + 2 x)

= 3 (24 x^{5} - 16 x^{3} + 2 x)

d er i v a t i v e 2 sin (θ)

\frac{\partial}{\partial x} (x^{2} + 2 x y + 2 y^{2} - 8 x + 8 y)

\int_{1}^{\infty} \frac{1}{x ^{2} + 3} d x

d er i v a t i v e y = 3 1.6 x^{2} + 4.9

d er i v a t i v e f (t) = \frac{1}{2} (9 t^{2} + t)^{- 3}