derivative f(x)=(x+5)(9sqrt(x)+5)

解答

导数

f (x) = (x + 5) (9 x + 5)

\frac{27 x + 45}{2 x} + 5

求解步骤

\frac{d}{d x} ((x + 5) (9 x + 5))

使用微分乘法定则:

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

f = x + 5, g = 9 x + 5

= \frac{d}{d x} (x + 5) (9 x + 5) + \frac{d}{d x} (9 x + 5) (x + 5)

\frac{d}{d x} (x + 5) = 1

\frac{d}{d x} (9 x + 5) = \frac{9}{2 x}

= 1 \cdot (9 x + 5) + \frac{9}{2 x} (x + 5)

化简

1 \cdot (9 x + 5) + \frac{9}{2 x} (x + 5) : \frac{27 x + 45}{2 x} + 5

= \frac{27 x + 45}{2 x} + 5

\frac{d}{d x} ((cos (x) + 2)^{3} (2 x)^{(- 3 x)})

\int (e^{- x^{2}}) d x

\int t e^{- t} d t

y^{^{''}} + 4 y^{^{'}} = - 6 x - 3

\frac{\partial}{\partial x} (- sin (x) cos (y))