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Beliebt Rechnen >

derivative of x^3+x^2y+x

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (x^{2} y) + \frac{d x}{d x}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (x^{2} y) = 2 x y + \frac{d y}{d x} x^{2}

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

= 3 x^{2} + 2 x y + \frac{d y}{d x} x^{2} + 1

Beliebte Beispiele

tangent f(x)=x^4-20x^2+64,\at x=1

t an g e n t f (x) = x^{4} - 20 x^{2} + 64, at x = 1

(\partial)/(\partial x)(-y/(sqrt(y^2-x^2)))

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

integral of 2x-3

\int 2 x - 3 d x

derivative f(x)=-x+7/x+1\at x

d er i v a t i v e f (x) = - x + \frac{7}{x} + 1 at x

derivative sqrt((x^2*5^x)^7)

d er i v a t i v e (x^{2} \cdot 5^{x})^{7}