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Beliebt Rechnen >

derivative of xy^'

Lösung

\frac{d}{d x} (x y^{^{'}})

Lösung

y^{'} +' x \frac{d y}{d x} y^{' - 1}

Schritte zur Lösung

\frac{d}{d x} (x y^{^{'}})

Wende die Produktregel an:

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

f = x, g = y^{^{'}}

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

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

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

= 1 \cdot y^{^{^{'}}} +^{^{'}} \frac{d y}{d x} y^{^{^{'}} - 1} x

Vereinfache

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

Beliebte Beispiele

tangent y=x^4+7x^2-x,(1,7)

t an g e n t y = x^{4} + 7 x^{2} - x, (1, 7)

integral from 0 to 2 of 2sec((pix)/6)

\int_{0}^{2} 2 sec (\frac{π x}{6}) d x

t a y l or 2^{x}, 1

integral of 1/(θ^2)sin(1/θ)cos(1/θ)

\int \frac{1}{θ ^{2}} sin (\frac{1}{θ}) cos (\frac{1}{θ}) d θ

\frac{d}{d t} (e^{5 t})