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Beliebt Rechnen >

derivative of x^5y

Lösung

\frac{d}{d x} (x^{5} y)

Lösung

5 x^{4} y + \frac{d y}{d x} x^{5}

Schritte zur Lösung

\frac{d}{d x} (x^{5} y)

Wende die Produktregel an:

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

f = x^{5}, g = y

= \frac{d}{d x} (x^{5}) y + \frac{d y}{d x} x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 5 x^{4} y + \frac{d y}{d x} x^{5}

Beliebte Beispiele

integral of (cos(x))/(4+sin(x))

\int \frac{cos ( x )}{4 + sin ( x )} d x

integral of (2-5x)/(x^6)

\int \frac{2 - 5 x}{x ^{6}} d x

(dy)/(dx)+(2xy)/(x^2+1)=x

\frac{d y}{d x} + \frac{2 x y}{x ^{2} + 1} = x

tangent 3/(x^2)

t an g e n t \frac{3}{x ^{2}}

integral of 1/(x^2sqrt(x^2+9))

\int \frac{1}{x ^{2} x ^{2} + 9} d x