derivative 5x^4sqrt(25-x^2)

解答

导数

5 x^{4} 25 - x^{2}

\frac{5 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

求解步骤

\frac{d}{d x} (5 x^{4} 25 - x^{2})

将常数提出:

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

= 5 \frac{d}{d x} (x^{4} 25 - x^{2})

使用微分乘法定则:

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

f = x^{4}, g = 25 - x^{2}

= 5 (\frac{d}{d x} (x^{4}) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x^{4})

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

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 5 (4 x^{3} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{4})

化简

5 (4 x^{3} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{4}) : \frac{5 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

= \frac{5 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

\frac{\partial}{\partial y} (\frac{( x + y )}{( y + z )})

\frac{\partial}{\partial x} (\frac{x}{x ^{6} - y ^{3}})

\frac{d y}{d x} = 4 x + y, y (0) = 9

\frac{d}{d x} (x^{16})

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