derivative [3(3x^5+6)^3](12x^3)

Lösung

ableitung von

[3 (3 x^{5} + 6)^{3}] (12 x^{3})

36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{7} (3 x^{5} + 6)^{2})

Schritte zur Lösung

\frac{d}{d x} ((3 (3 x^{5} + 6)^{3}) \cdot 12 x^{3})

Vereinfache

(3 (3 x^{5} + 6)^{3}) \cdot 12 x^{3} : 36 x^{3} (3 x^{5} + 6)^{3}

= \frac{d}{d x} (36 x^{3} (3 x^{5} + 6)^{3})

Entferne die Konstante:

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

= 36 \frac{d}{d x} (x^{3} (3 x^{5} + 6)^{3})

Wende die Produktregel an:

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

f = x^{3}, g = (3 x^{5} + 6)^{3}

= 36 (\frac{d}{d x} (x^{3}) (3 x^{5} + 6)^{3} + \frac{d}{d x} ((3 x^{5} + 6)^{3}) x^{3})

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

\frac{d}{d x} ((3 x^{5} + 6)^{3}) = 45 x^{4} (3 x^{5} + 6)^{2}

= 36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{4} (3 x^{5} + 6)^{2} x^{3})

45 x^{4} (3 x^{5} + 6)^{2} x^{3} = 45 x^{7} (3 x^{5} + 6)^{2}

= 36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{7} (3 x^{5} + 6)^{2})

a re a x = 9 y^{3}, x = 23 y^{2}

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

d er i v a t i v e f (x) = (2 x + 1)^{5}

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

x^{3} y^{^{'}} + 4 x^{2} y = e^{- x}