derivative of x(x^4+9^3)

解答

\frac{d}{d x} (x (x^{4} + 9)^{3})

(x^{4} + 9)^{3} + 12 x^{4} (x^{4} + 9)^{2}

求解步骤

\frac{d}{d x} (x (x^{4} + 9)^{3})

使用微分乘法定则:

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

f = x, g = (x^{4} + 9)^{3}

= \frac{d x}{d x} (x^{4} + 9)^{3} + \frac{d}{d x} ((x^{4} + 9)^{3}) x

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

\frac{d}{d x} ((x^{4} + 9)^{3}) = 12 x^{3} (x^{4} + 9)^{2}

= 1 \cdot (x^{4} + 9)^{3} + 12 x^{3} (x^{4} + 9)^{2} x

化简

1 \cdot (x^{4} + 9)^{3} + 12 x^{3} (x^{4} + 9)^{2} x : (x^{4} + 9)^{3} + 12 x^{4} (x^{4} + 9)^{2}

= (x^{4} + 9)^{3} + 12 x^{4} (x^{4} + 9)^{2}

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

in v erse l a pl a ce \frac{( 12 s + 8 )}{( s - 1 ) ^{5}}

(1 - x) y^{^{'}} = y^{2}

d er i v a t i v e \frac{- 8}{5 x + 5}

\frac{d}{d x} (tan (2))