derivative of (1+x^4tan(x)^{-5})

解答

\frac{d}{d x} ((1 + x^{4} tan (x))^{- 5})

- \frac{5 ( x ^{4} sec ^{2} ( x ) + 4 x ^{3} tan ( x ) )}{( 1 + x ^{4} tan ( x ) ) ^{6}}

求解步骤

\frac{d}{d x} ((1 + x^{4} tan (x))^{- 5})

使用连锁律:

- \frac{5}{( 1 + x ^{4} tan ( x ) ) ^{6}} \frac{d}{d x} (1 + x^{4} tan (x))

= - \frac{5}{( 1 + x ^{4} tan ( x ) ) ^{6}} \frac{d}{d x} (1 + x^{4} tan (x))

\frac{d}{d x} (1 + x^{4} tan (x)) = x^{4} sec^{2} (x) + 4 x^{3} tan (x)

= - \frac{5}{( 1 + x ^{4} tan ( x ) ) ^{6}} (x^{4} sec^{2} (x) + 4 x^{3} tan (x))

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{5 ( x ^{4} sec ^{2} ( x ) + 4 x ^{3} tan ( x ) )}{( 1 + x ^{4} tan ( x ) ) ^{6}}

x \to 4 + lim (\frac{3 + x}{4 - x})

d er i v a t i v e f (x) = \frac{3 x ^{5}}{5} - \frac{10 x ^{4}}{3}

\frac{d y}{d x} = \frac{3 x ^{2}}{y}

l a pl a ce t r an s f or m 2 sin^{2} (t)

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