d/(dq)(({R}(q))({R}(q)(q^4+1)^5))

解答

\frac{d}{d q} ((R (q)) (R (q) (q^{4} + 1)^{5}))

2 R (q) \frac{d}{d q} (R (q)) (q^{4} + 1)^{5} + 20 q^{3} (q^{4} + 1)^{4} R (q)^{2}

求解步骤

\frac{d}{d q} ((R (q)) (R (q) (q^{4} + 1)^{5}))

化简

(R (q)) (R (q) (q^{4} + 1)^{5}) : R (q)^{2} (q^{4} + 1)^{5}

= \frac{d}{d q} (R (q)^{2} (q^{4} + 1)^{5})

使用微分乘法定则:

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

f = R (q)^{2}, g = (q^{4} + 1)^{5}

= \frac{d}{d q} (R (q)^{2}) (q^{4} + 1)^{5} + \frac{d}{d q} ((q^{4} + 1)^{5}) R (q)^{2}

\frac{d}{d q} (R (q)^{2}) = 2 R (q) \frac{d}{d q} (R (q))

\frac{d}{d q} ((q^{4} + 1)^{5}) = 20 q^{3} (q^{4} + 1)^{4}

= 2 R (q) \frac{d}{d q} (R (q)) (q^{4} + 1)^{5} + 20 q^{3} (q^{4} + 1)^{4} R (q)^{2}

e x p an d (2 sin (x) + 1) (cos (x) + 1)

e x p an d (5 x + 3)^{6} d x

e x p an d (6 x^{2} - 3 x^{3}) d x

e x p an d \frac{x - 4}{x ( x - 5 )}

s im pl i f y (x + 1) (\frac{x}{x + 1} + 1)