derivative of 6^4x^3+x^5-180sqrt(4x^2)

Lösung

\frac{d}{d x} (6^{4} x^{3} + x^{5} - 180 4 x^{2})

3888 x^{2} + 5 x^{4} - \frac{360 x}{∣ x ∣}

Schritte zur Lösung

\frac{d}{d x} (6^{4} x^{3} + x^{5} - 180 4 x^{2})

Vereinfache

6^{4} x^{3} + x^{5} - 180 4 x^{2} : 1296 x^{3} + x^{5} - 360 x^{2}

= \frac{d}{d x} (1296 x^{3} + x^{5} - 360 x^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (1296 x^{3}) + \frac{d}{d x} (x^{5}) - \frac{d}{d x} (360 x^{2})

\frac{d}{d x} (1296 x^{3}) = 3888 x^{2}

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

\frac{d}{d x} (360 x^{2}) = \frac{360 x}{∣ x ∣}

= 3888 x^{2} + 5 x^{4} - \frac{360 x}{∣ x ∣}

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

\int_{- 7}^{7} (1 + 49 - x^{2}) d x

\frac{d y}{d x} = \frac{x ^{2} + 2 y ^{2}}{x y}

t an g e n t f (x) = \frac{1}{( x - 5 )}, at x = - 3

in v erse l a pl a ce \frac{2 s + 1}{s ^{2} - 2 s + 2}