derivative of sin(x(x^2-27x+6))

Lösung

\frac{d}{d x} (sin (x) (x^{2} - 27 x + 6))

cos (x) (x^{2} - 27 x + 6) + (2 x - 27) sin (x)

Schritte zur Lösung

\frac{d}{d x} (sin (x) (x^{2} - 27 x + 6))

Wende die Produktregel an:

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

f = sin (x), g = x^{2} - 27 x + 6

= \frac{d}{d x} (sin (x)) (x^{2} - 27 x + 6) + \frac{d}{d x} (x^{2} - 27 x + 6) sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (x^{2} - 27 x + 6) = 2 x - 27

= cos (x) (x^{2} - 27 x + 6) + (2 x - 27) sin (x)

49 y^{^{''}} + 14 y^{^{'}} + y = 0

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

\int_{- 2}^{1} (8 x^{3} - 3 x^{2}) d x

\frac{d y}{d x} = 3 x e^{y}

t an g e n t (7 - 6 x)^{\frac{1}{2}}, at x = - 1