derivative of cot^4(x-csc^4(x))

解答

\frac{d}{d x} (cot^{4} (x) - csc^{4} (x))

4 csc^{2} (x) cot (x)

求解步骤

\frac{d}{d x} (cot^{4} (x) - csc^{4} (x))

使用微分加减法定则:

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

= \frac{d}{d x} (cot^{4} (x)) - \frac{d}{d x} (csc^{4} (x))

\frac{d}{d x} (cot^{4} (x)) = - 4 cot^{3} (x) csc^{2} (x)

\frac{d}{d x} (csc^{4} (x)) = - 4 csc^{4} (x) cot (x)

= - 4 cot^{3} (x) csc^{2} (x) - (- 4 csc^{4} (x) cot (x))

化简

- 4 cot^{3} (x) csc^{2} (x) - (- 4 csc^{4} (x) cot (x)) : 4 csc^{2} (x) cot (x)

= 4 csc^{2} (x) cot (x)

d er i v a t i v e y = 2^{2 x}

d er i v a t i v e y = e^{in (x^{2} + 1)}

x \to 2 lim (\frac{3 3 x ^{2} - 2 x - 8}{( x + 2 ) ^{3}})

t a y l or \frac{1}{( 1 + x ^{2} )}

\int \frac{x ^{2}}{9 - x ^{2}} d x