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Beliebt Rechnen >

(\partial)/(\partial x)(xln(x+6y))

Lösung

\frac{\partial}{\partial x} (x ln (x + 6 y))

Lösung

ln (x + 6 y) + \frac{x}{x + 6 y}

Schritte zur Lösung

\frac{\partial}{\partial x} (x ln (x + 6 y))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = ln (x + 6 y)

= \frac{\partial}{\partial x} (x) ln (x + 6 y) + \frac{\partial}{\partial x} (ln (x + 6 y)) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (ln (x + 6 y)) = \frac{1}{x + 6 y}

= 1 \cdot ln (x + 6 y) + \frac{1}{x + 6 y} x

Vereinfache

1 \cdot ln (x + 6 y) + \frac{1}{x + 6 y} x : ln (x + 6 y) + \frac{x}{x + 6 y}

= ln (x + 6 y) + \frac{x}{x + 6 y}

Beliebte Beispiele

y^{''}-5y^'=e^{5x}

y^{^{''}} - 5 y^{^{'}} = e^{5 x}

erweitern 6/((w^2-8)^4)

e x p an d \frac{6}{( w ^{2} - 8 ) ^{4}}

derivative f(x)=7e^{-x^2}

d er i v a t i v e f (x) = 7 e^{- x^{2}}

fläche x^2+2x,x+2,-2,1

a re a x^{2} + 2 x, x + 2, - 2, 1

integral from 49.75 to x of 2

\int_{49.75}^{x} 2 d x