derivative of x^ay^b

Lösung

\frac{d}{d x} (x^{a} y^{b})

a x^{a - 1} y^{b} + b y^{b - 1} \frac{d y}{d x} x^{a}

Schritte zur Lösung

\frac{d}{d x} (x^{a} y^{b})

Wende die Produktregel an:

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

f = x^{a}, g = y^{b}

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

\frac{d}{d x} (x^{a}) = a x^{a - 1}

\frac{d}{d x} (y^{b}) = b y^{b - 1} \frac{d y}{d x}

= a x^{a - 1} y^{b} + b y^{b - 1} \frac{d y}{d x} x^{a}

d er i v a t i v e (\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 8 x^{3})

\int 7 x^{3} (x - 5)^{- 4} d x

in v erse l a pl a ce \frac{2}{s} + \frac{3}{s + 1}

\frac{d}{d x} (\frac{( 4 x ^{2} + 6 x + 4 )}{x})

t a y l or \frac{( e ^{t} )}{1 + t}