(\partial)/(\partial x)(ysqrt(1+x^7))

解答

\frac{\partial}{\partial x} (y 1 + x^{7})

\frac{7 y x ^{6}}{2 1 + x ^{7}}

求解步骤

\frac{\partial}{\partial x} (y 1 + x^{7})

将

y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (1 + x^{7})

使用连锁律:

\frac{1}{2 1 + x ^{7}} \frac{\partial}{\partial x} (1 + x^{7})

= \frac{1}{2 1 + x ^{7}} \frac{\partial}{\partial x} (1 + x^{7})

\frac{\partial}{\partial x} (1 + x^{7}) = 7 x^{6}

= y \frac{1}{2 1 + x ^{7}} \cdot 7 x^{6}

化简

y \frac{1}{2 1 + x ^{7}} \cdot 7 x^{6} : \frac{7 y x ^{6}}{2 1 + x ^{7}}

= \frac{7 y x ^{6}}{2 1 + x ^{7}}

\int \frac{11 x ^{2}}{( 144 + x ^{2} ) ^{2}} d x

\frac{d}{d x} (x^{6} ln (7 x))

d er i v a t i v e y = \frac{1}{( x ^{2} - 1 ) ( x ^{2} + 3 x + 3 )}

\frac{d}{d x} (x^{\frac{9}{4}})

d er i v a t i v e f (θ) = 11 θ