derivative of sqrt(x^2+4xy+y^6)-8

Lösung

\frac{d}{d x} (x^{2} + 4 x y + y^{6} - 8)

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

Schritte zur Lösung

\frac{d}{d x} (x^{2} + 4 x y + y^{6} - 8)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{2} + 4 x y + y^{6}) - \frac{d}{d x} (8)

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

\frac{d}{d x} (8) = 0

= \frac{x + 2 ( x \frac{d y}{d x} + y ) + 3 y ^{5} \frac{d y}{d x}}{x ^{2} + 4 x y + y ^{6}} - 0

Vereinfache

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

\int_{3}^{4} 9 x d x

\int \frac{3 x ^{2} - 4 x + 5}{( x - 1 ) ( x ^{2} + 1 )} d x

\frac{d}{d x} ((sin (2 x))^{x})

\int 3 (5^{1 - 2 x}) d x

\frac{d}{d x} (40 x)