derivative of (15x^7+27x^5/(3x))

Lösung

\frac{d}{d x} (\frac{15 x ^{7} + 27 x ^{5}}{3 x})

30 x^{5} + 36 x^{3}

Schritte zur Lösung

\frac{d}{d x} (\frac{15 x ^{7} + 27 x ^{5}}{3 x})

Vereinfache

\frac{15 x ^{7} + 27 x ^{5}}{3 x} : x^{4} (5 x^{2} + 9)

= \frac{d}{d x} (x^{4} (5 x^{2} + 9))

Wende die Produktregel an:

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

f = x^{4}, g = 5 x^{2} + 9

= \frac{d}{d x} (x^{4}) (5 x^{2} + 9) + \frac{d}{d x} (5 x^{2} + 9) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (5 x^{2} + 9) = 10 x

= 4 x^{3} (5 x^{2} + 9) + 10 x x^{4}

Vereinfache

4 x^{3} (5 x^{2} + 9) + 10 x x^{4} : 30 x^{5} + 36 x^{3}

= 30 x^{5} + 36 x^{3}

y = x^{3 x}

d er i v a t i v e x^{2} + y^{2}

x \frac{d y}{d x} - 3 y = 7 x^{4}, y (1) = 2

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

\int ln (x^{2} - x - 6) d x