derivative of (d/(dx(x^5-5))/(x+1))

Lösung

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

\frac{20 x ^{3}}{x + 1}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( \frac{d}{d x} ( x ^{5} - 5 ) ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) \frac{d}{d x} ( x ^{5} - 5 )}{( x + 1 ) ^{2}}

\frac{d}{d x} (\frac{d}{d x} (x^{5} - 5)) = 20 x^{3}

\frac{d}{d x} (x^{5} - 5) = 5 x^{4}

\frac{d ^{2}}{d x ^{2}} (x + 1) = 0

\frac{d}{d x} (x^{5} - 5) = 5 x^{4}

= \frac{20 x ^{3} ( x + 1 ) - 0 \cdot 5 x ^{4}}{( x + 1 ) ^{2}}

Vereinfache

\frac{20 x ^{3} ( x + 1 ) - 0 \cdot 5 x ^{4}}{( x + 1 ) ^{2}} : \frac{20 x ^{3}}{x + 1}

= \frac{20 x ^{3}}{x + 1}

\int e^{- \frac{1}{4} x^{2}} x d x

\int 2 x (x^{2} + 17)^{13} d x

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

a re a y = 7 x^{2}, y = x^{2} + 3

t an g e n t f (x) = \frac{10 x}{x ^{2} - 6}, at x = 4