derivative of x(3x+1^5)

Lösung

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

(3 x + 1)^{5} + 15 x (3 x + 1)^{4}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((3 x + 1)^{5}) = 15 (3 x + 1)^{4}

= 1 \cdot (3 x + 1)^{5} + 15 (3 x + 1)^{4} x

Vereinfache

= (3 x + 1)^{5} + 15 x (3 x + 1)^{4}

x \to 1 lim (\frac{sin ( x - 1 )}{x})

\int \frac{ln ( 2 x )}{3 x} d x

t an g e n t f (x) = 3 sin (x), at x = - \frac{π}{4}

d er i v a t i v e y = 80 (1 - e^{- 0.041 x})

\frac{\partial}{\partial x} (y (x^{2} + y)^{6})