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

Lösung

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

5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = (x^{2} - 4)^{2}, g = x - 1

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

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

\frac{d}{d x} (x - 1) = 1

= 4 x (x^{2} - 4) (x - 1) + 1 \cdot (x^{2} - 4)^{2}

Vereinfache

4 x (x^{2} - 4) (x - 1) + 1 \cdot (x^{2} - 4)^{2} : 5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16

= 5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16

d er i v a t i v e \frac{( 1 - 5 t )}{2 + t}

\frac{\partial}{\partial x} (\frac{1}{2 π t} e^{- \frac{( x - y ) ^{2}}{2 t}})

x \to 1 - lim (2 x - 1)

d er i v a t i v e f (x) = \frac{4 x}{x ^{2} + 4}

\int \frac{28}{1 - cos ( 4 x )} d x