derivative of (3-2x^2^2sqrt(2x^2+1))

Lösung

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

\frac{40 x ^{5} - 56 x ^{3} - 6 x}{2 x ^{2} + 1}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} ((3 - 2 x^{2})^{2}) = - 8 x (3 - 2 x^{2})

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

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

Vereinfache

(- 8 x (3 - 2 x^{2})) 2 x^{2} + 1 + \frac{2 x}{2 x ^{2} + 1} (3 - 2 x^{2})^{2} : \frac{40 x ^{5} - 56 x ^{3} - 6 x}{2 x ^{2} + 1}

= \frac{40 x ^{5} - 56 x ^{3} - 6 x}{2 x ^{2} + 1}

d er i v a t i v e \frac{x}{x - 4}

d er i v a t i v e \frac{- 2 x ^{2} + 9}{9 - x ^{2}}

\int_{7}^{8} (\frac{1}{x ^{2}} - 1) d x

(\frac{ln ( x )}{x ^{2}})^{^{'}}

\frac{\partial}{\partial x} (cos^{7} (x^{9} y^{5}))