derivative of sin^6(pix)

解答

\frac{d}{d x} (sin^{6} (π x))

6 π sin^{5} (π x) cos (π x)

求解步骤

\frac{d}{d x} (sin^{6} (π x))

使用连锁律:

6 (sin (π x))^{5} \frac{d}{d x} (sin (π x))

= 6 (sin (π x))^{5} \frac{d}{d x} (sin (π x))

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

= 6 (sin (π x))^{5} cos (π x) π

化简

= 6 π sin^{5} (π x) cos (π x)

\int \frac{x ^{2} + x}{( x - 3 ) ( x ^{2} + 1 )} d x

\int \frac{7 x ^{3}}{7 + x ^{2}} d x

\frac{d}{d x} (x^{3} + x^{2} + 1)

\frac{d}{d x} (\frac{x}{1 + 5 x ^{2}})

(t - 1)^{2} y^{^{'}} + 3 (t - 1) y = t + 2