derivative xsqrt(a+bx)

Lösung

ableitung von

x a + b x

\frac{3 b x + 2 a}{2 a + b x}

Schritte zur Lösung

\frac{d}{d x} (x a + b x)

Wende die Produktregel an:

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

f = x, g = a + b x

= \frac{d x}{d x} a + b x + \frac{d}{d x} (a + b x) x

\frac{d x}{d x} = 1

\frac{d}{d x} (a + b x) = \frac{b}{2 a + b x}

= 1 \cdot a + b x + \frac{b}{2 a + b x} x

Vereinfache

1 \cdot a + b x + \frac{b}{2 a + b x} x : \frac{3 b x + 2 a}{2 a + b x}

= \frac{3 b x + 2 a}{2 a + b x}

\int \frac{ln ( 6 x )}{x ^{4}} d x

\int_{1}^{2} x d x

\frac{\partial}{\partial z} (arctan (\frac{y}{x}))

\int \frac{x ^{2} - x + 10}{( x + 2 ) ( x ^{2} + 4 )} d x

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