derivative of 3x-5cos^2(pix)

解答

\frac{d}{d x} (3 x - 5 cos^{2} (π x))

3 + 10 π cos (π x) sin (π x)

求解步骤

\frac{d}{d x} (3 x - 5 cos^{2} (π x))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x) - \frac{d}{d x} (5 cos^{2} (π x))

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

\frac{d}{d x} (5 cos^{2} (π x)) = - 10 π cos (π x) sin (π x)

= 3 - (- 10 π cos (π x) sin (π x))

化简

= 3 + 10 π cos (π x) sin (π x)

\int \frac{1}{x ^{2} + 6 x + 34} d x

\int_{1}^{3} \frac{ln ( x )}{x} d x

s l o p e (2 x + 2 y)^{3} = 8 x^{3} + 8 y^{3} (- 1.1)

\int_{1}^{5} \frac{5}{x} d x

d er i v a t i v e \frac{3}{4 x + 6} + 4 x^{2}