derivative of (3x^2-5^4(2x^2+1)^3)

Lösung

\frac{d}{d x} ((3 x^{2} - 5)^{4} (2 x^{2} + 1)^{3})

24 x (3 x^{2} - 5)^{3} (2 x^{2} + 1)^{3} + 12 x (2 x^{2} + 1)^{2} (3 x^{2} - 5)^{4}

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} - 5)^{4} (2 x^{2} + 1)^{3})

Wende die Produktregel an:

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

f = (3 x^{2} - 5)^{4}, g = (2 x^{2} + 1)^{3}

= \frac{d}{d x} ((3 x^{2} - 5)^{4}) (2 x^{2} + 1)^{3} + \frac{d}{d x} ((2 x^{2} + 1)^{3}) (3 x^{2} - 5)^{4}

\frac{d}{d x} ((3 x^{2} - 5)^{4}) = 24 x (3 x^{2} - 5)^{3}

\frac{d}{d x} ((2 x^{2} + 1)^{3}) = 12 x (2 x^{2} + 1)^{2}

= 24 x (3 x^{2} - 5)^{3} (2 x^{2} + 1)^{3} + 12 x (2 x^{2} + 1)^{2} (3 x^{2} - 5)^{4}

d er i v a t i v e f (x) = tan (sec (cos (x)))

\frac{d}{d x} (tan^{s e c (\frac{1}{x})} (\frac{1}{x}))

d er i v a t i v e f (x) = x^{4} - 6 x^{3}

\frac{d}{d x} (ln (x^{2} \cdot e^{x^{2} + 1}))

t a y l or (1 + \frac{1}{x})^{- 2}