derivative x^2sqrt(36-x^2)

解答

导数

x^{2} 36 - x^{2}

\frac{- 3 x ^{3} + 72 x}{36 - x ^{2}}

求解步骤

\frac{d}{d x} (x^{2} 36 - x^{2})

使用微分乘法定则:

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

f = x^{2}, g = 36 - x^{2}

= \frac{d}{d x} (x^{2}) 36 - x^{2} + \frac{d}{d x} (36 - x^{2}) x^{2}

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

\frac{d}{d x} (36 - x^{2}) = - \frac{x}{36 - x ^{2}}

= 2 x 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x^{2}

化简

2 x 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 72 x}{36 - x ^{2}}

= \frac{- 3 x ^{3} + 72 x}{36 - x ^{2}}

x^{2} d y - 2 x y d x = x^{4} cos (2 x) d x

d er i v a t i v e (t + e^{t}) (6 - t)

y^{^{''}} + 5 y^{^{'}} + 6 y = 6

\frac{d}{d t} (t^{2})

d er i v a t i v e y = e^{- s i n (x)}