derivative of 9xsin(pix)

解答

\frac{d}{d x} (9 x sin (π x))

9 (sin (π x) + π x cos (π x))

求解步骤

\frac{d}{d x} (9 x sin (π x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (x sin (π x))

使用微分乘法定则:

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

f = x, g = sin (π x)

= 9 (\frac{d x}{d x} sin (π x) + \frac{d}{d x} (sin (π x)) x)

\frac{d x}{d x} = 1

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

= 9 (1 \cdot sin (π x) + cos (π x) π x)

化简

= 9 (sin (π x) + π x cos (π x))

x \to 1 lim (\frac{x ^{6} - 1}{x - 1})

\int_{0}^{1} \frac{9}{x ^{5}} d x

\int \frac{1}{( x ^{2} - 6 x + 11 ) ^{2}} d x

d er i v a t i v e y = - 8^{5 x^{2} - 4}

x \to - 1 lim (3 x^{4} - 2 x^{3} + 4 x)