derivative (3sqrt(x)+7)x^2

Lösung

ableitung von

(3 x + 7) x^{2}

\frac{3 x ^{\frac{3}{2}}}{2} + 2 x (3 x + 7)

Schritte zur Lösung

\frac{d}{d x} ((3 x + 7) x^{2})

Wende die Produktregel an:

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

f = 3 x + 7, g = x^{2}

= \frac{d}{d x} (3 x + 7) x^{2} + \frac{d}{d x} (x^{2}) (3 x + 7)

\frac{d}{d x} (3 x + 7) = \frac{3}{2 x}

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

= \frac{3}{2 x} x^{2} + 2 x (3 x + 7)

\frac{3}{2 x} x^{2} = \frac{3 x ^{\frac{3}{2}}}{2}

= \frac{3 x ^{\frac{3}{2}}}{2} + 2 x (3 x + 7)

\frac{d}{d x} (- \frac{32}{x ^{3}} + \frac{4}{x ^{2}})

\int_{2}^{4} \frac{x ^{2} + 1}{x ^{2} - 5} d x

\int x^{3} cos (x^{2}) d x

\int x x - 9 d x

t an g e n t 3 x y^{3} + 4 x y = 28, (4, 1)