derivative of (x+5cos(x))

解答

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

cos (x) - sin (x) (x + 5)

求解步骤

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

使用微分乘法定则:

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

f = x + 5, g = cos (x)

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

= 1 \cdot cos (x) + (- sin (x)) (x + 5)

化简

= cos (x) - sin (x) (x + 5)

y ln (y) d x + x d y = 0

t an g e n t y = x^{3} - 3 x^{2} - 9 x + 27, at x = 4

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

\int_{1}^{8} \frac{3}{x} d x

\frac{d}{d x} (e^{x^{\frac{1}{2}}})