derivative of sin^4(x+cos^4(x))

解答

\frac{d}{d x} (sin^{4} (x) + cos^{4} (x))

- 4 cos (x) sin (x) cos (2 x)

求解步骤

\frac{d}{d x} (sin^{4} (x) + cos^{4} (x))

使用微分加减法定则:

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

= \frac{d}{d x} (sin^{4} (x)) + \frac{d}{d x} (cos^{4} (x))

\frac{d}{d x} (sin^{4} (x)) = 4 sin^{3} (x) cos (x)

\frac{d}{d x} (cos^{4} (x)) = - 4 cos^{3} (x) sin (x)

= 4 sin^{3} (x) cos (x) - 4 cos^{3} (x) sin (x)

化简

4 sin^{3} (x) cos (x) - 4 cos^{3} (x) sin (x) : - 4 cos (x) sin (x) cos (2 x)

= - 4 cos (x) sin (x) cos (2 x)

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

\frac{d}{d x} (x^{2} (20 - x)^{3})

\int \frac{5 x + 6}{( x - 2 ) ( 3 x + 1 ) ^{2}} d x

d er i v a t i v e f (y) = e^{t a n (x)}

\frac{d y}{d x} = \frac{y + 4}{2 - y}