derivative of xsqrt(x^2+36)

Lösung

\frac{d}{d x} (x x^{2} + 36)

\frac{2 x ^{2} + 36}{x ^{2} + 36}

Schritte zur Lösung

\frac{d}{d x} (x x^{2} + 36)

Wende die Produktregel an:

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

f = x, g = x^{2} + 36

= \frac{d x}{d x} x^{2} + 36 + \frac{d}{d x} (x^{2} + 36) x

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

\frac{d}{d x} (x^{2} + 36) = \frac{x}{x ^{2} + 36}

= 1 \cdot x^{2} + 36 + \frac{x}{x ^{2} + 36} x

Vereinfache

1 \cdot x^{2} + 36 + \frac{x}{x ^{2} + 36} x : \frac{2 x ^{2} + 36}{x ^{2} + 36}

= \frac{2 x ^{2} + 36}{x ^{2} + 36}

\frac{d}{d x} (\frac{( x - x )}{x ^{\frac{1}{5}}})

d er i v a t i v e 100 - \frac{200}{t ^{2} + 4}

d er i v a t i v e - \frac{5}{x ^{5}}

y^{^{''}} + 25 y = cos (4 t)

n = 1 \sum \infty \frac{( n )}{2 ^{n}}