derivative of xsqrt(x^2-16)

Lösung

\frac{d}{d x} (x x^{2} - 16)

\frac{2 x ^{2} - 16}{x ^{2} - 16}

Schritte zur Lösung

\frac{d}{d x} (x x^{2} - 16)

Wende die Produktregel an:

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

f = x, g = x^{2} - 16

= \frac{d x}{d x} x^{2} - 16 + \frac{d}{d x} (x^{2} - 16) x

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

\frac{d}{d x} (x^{2} - 16) = \frac{x}{x ^{2} - 16}

= 1 \cdot x^{2} - 16 + \frac{x}{x ^{2} - 16} x

Vereinfache

1 \cdot x^{2} - 16 + \frac{x}{x ^{2} - 16} x : \frac{2 x ^{2} - 16}{x ^{2} - 16}

= \frac{2 x ^{2} - 16}{x ^{2} - 16}

in v erse l a pl a ce \frac{10}{s ^{2} + s + 10}

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

t an g e n t f (x) = \frac{3}{x + 1}, at x = 7

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 60 cos (8 t)

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