derivative of sqrt(1-4x)x^3

Lösung

\frac{d}{d x} (1 - 4 x x^{3})

\frac{- 14 x ^{3} + 3 x ^{2}}{1 - 4 x}

Schritte zur Lösung

\frac{d}{d x} (1 - 4 x x^{3})

Wende die Produktregel an:

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

f = 1 - 4 x, g = x^{3}

= \frac{d}{d x} (1 - 4 x) x^{3} + \frac{d}{d x} (x^{3}) 1 - 4 x

\frac{d}{d x} (1 - 4 x) = - \frac{2}{1 - 4 x}

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

= (- \frac{2}{1 - 4 x}) x^{3} + 3 x^{2} 1 - 4 x

Vereinfache

(- \frac{2}{1 - 4 x}) x^{3} + 3 x^{2} 1 - 4 x : \frac{- 14 x ^{3} + 3 x ^{2}}{1 - 4 x}

= \frac{- 14 x ^{3} + 3 x ^{2}}{1 - 4 x}

cos (x) y^{^{'}} + y = sin (x)

l a pl a ce t r an s f or m e^{3 t} (t^{2} + 4)

\int_{0}^{4} 2 x d x

\int θ^{3} sin (θ^{2}) d θ

\int \frac{x}{( 2 x + 1 ) ^{2}} d x