(xcos(x))^'

解答

(x cos (x))^{^{'}}

cos (x) - x sin (x)

求解步骤

(x cos (x))^{'}

使用微分乘法定则:

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

f = x, g = cos (x)

= x^{^{'}} cos (x) + (cos (x))^{^{'}} x

x^{'} = 1

(cos (x))^{'} = - sin (x)

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

化简

= cos (x) - x sin (x)

d er i v a t i v e f (x) = x^{3} (3 - x^{2})

d er i v a t i v e f (x) = \frac{x}{x ^{2} - 7}

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

n \to 2 lim (\frac{1}{n ^{2}})

x \to 2 + lim (x^{2} - 4)