derivative f(x)=4x^3sqrt(x^4)

Lösung

ableitung von

f (x) = 4 x^{3} x^{4}

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x^{3}, g = x^{4}

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

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

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

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

2 x x^{3} = 2 x^{4}

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

\frac{d}{d x} (\frac{x sin ( 4 x )}{8})

6 y^{^{''}} + 4 y^{^{'}} + 7 y = 0

t an g e n t f (x) = 2 x^{2} + x - 1

y^{^{''}} + 9 y = 0, y (\frac{π}{2}) = 1, y^{^{'}} (\frac{π}{2}) = - 3

im pl i c i t \frac{d y}{d x}, 9 y + x = 4 y