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Beliebt Rechnen >

derivative y=(x^4+2)^2(x^3+4)^4

Lösung

ableitung von

y = (x^{4} + 2)^{2} (x^{3} + 4)^{4}

Lösung

8 x^{3} (x^{4} + 2) (x^{3} + 4)^{4} + 12 x^{2} (x^{3} + 4)^{3} (x^{4} + 2)^{2}

Schritte zur Lösung

\frac{d}{d x} ((x^{4} + 2)^{2} (x^{3} + 4)^{4})

Wende die Produktregel an:

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

f = (x^{4} + 2)^{2}, g = (x^{3} + 4)^{4}

= \frac{d}{d x} ((x^{4} + 2)^{2}) (x^{3} + 4)^{4} + \frac{d}{d x} ((x^{3} + 4)^{4}) (x^{4} + 2)^{2}

\frac{d}{d x} ((x^{4} + 2)^{2}) = 8 x^{3} (x^{4} + 2)

\frac{d}{d x} ((x^{3} + 4)^{4}) = 12 x^{2} (x^{3} + 4)^{3}

= 8 x^{3} (x^{4} + 2) (x^{3} + 4)^{4} + 12 x^{2} (x^{3} + 4)^{3} (x^{4} + 2)^{2}

Graph

Beliebte Beispiele

integral of-3x^2sin(pix)

\int - 3 x^{2} sin (π x) d x

y^{''}-2y^'-15y=3

y^{^{''}} - 2 y^{^{'}} - 15 y = 3

(\partial)/(\partial x)(x^{1/2}*y)

\frac{\partial}{\partial x} (x^{\frac{1}{2}} \cdot y)

derivative of (x-2/x ^4)

\frac{d}{d x} ((x - \frac{2}{x})^{4})

tangent f(x)=2x^2,\at x=0

t an g e n t f (x) = 2 x^{2}, at x = 0