(\partial)/(\partial x)(({f}(x,y))(4x-2y^4))

Lösung

\frac{\partial}{\partial x} ((f (x, y)) (4 x - 2 y^{4}))

\frac{\partial}{\partial x} (f (x, y)) (4 x - 2 y^{4}) + 4 f (x, y)

Schritte zur Lösung

\frac{\partial}{\partial x} ((f (x, y)) (4 x - 2 y^{4}))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = f (x, y), g = 4 x - 2 y^{4}

= \frac{\partial}{\partial x} (f (x, y)) (4 x - 2 y^{4}) + \frac{\partial}{\partial x} (4 x - 2 y^{4}) f (x, y)

\frac{\partial}{\partial x} (4 x - 2 y^{4}) = 4

= \frac{\partial}{\partial x} (f (x, y)) (4 x - 2 y^{4}) + 4 f (x, y)

e x p an d \frac{33 x ^{2}}{10} - \frac{6 x ^{2}}{5}

e x p an d \frac{x ( 2 x + 3 )}{x + 1}

e x p an d 81 + 18 \cdot 3^{2} - 54 \cdot 2^{- 2}

e x p an d \frac{6 x - 4}{x ( x + 4 )}

e x p an d x^{3} (x + 3 + 8 \cdot 3 = 0)