derivative of x^3(x-5^2)

Lösung

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

5 x^{4} - 40 x^{3} + 75 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = (x - 5)^{2}

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

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

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

= 3 x^{2} (x - 5)^{2} + 2 (x - 5) x^{3}

Vereinfache

3 x^{2} (x - 5)^{2} + 2 (x - 5) x^{3} : 5 x^{4} - 40 x^{3} + 75 x^{2}

= 5 x^{4} - 40 x^{3} + 75 x^{2}

h \to \infty lim (\frac{5 h ^{4} - 2 h ^{2} + 3}{3 h ^{3} + 2 h ^{2} + h})

\int (x^{2} + y^{2})^{(- \frac{3}{2})} d y

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

d er i v a t i v e y = 2 x^{2} + 1

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