(\partial)/(\partial x)((z)(x^3z^5+sin(y^7z^5)+6))

解答

\frac{\partial}{\partial x} ((z) (x^{3} z^{5} + sin (y^{7} z^{5}) + 6))

3 z^{6} x^{2}

求解步骤

\frac{\partial}{\partial x} ((z) (x^{3} z^{5} + sin (y^{7} z^{5}) + 6))

将

z, y

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} (x^{3} z^{5} + sin (y^{7} z^{5}) + 6)

使用微分加减法定则:

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

= z (\frac{\partial}{\partial x} (x^{3} z^{5}) + \frac{\partial}{\partial x} (sin (y^{7} z^{5})) + \frac{\partial}{\partial x} (6))

\frac{\partial}{\partial x} (x^{3} z^{5}) = 3 z^{5} x^{2}

\frac{\partial}{\partial x} (sin (y^{7} z^{5})) = 0

\frac{\partial}{\partial x} (6) = 0

= z (3 z^{5} x^{2} + 0 + 0)

化简

z (3 z^{5} x^{2} + 0 + 0) : 3 z^{6} x^{2}

= 3 z^{6} x^{2}

e x p an d \frac{1}{x \cdot ( x ^{2} + 1 )}

e x p an d 3 sin (\frac{π}{12} (t - 6)) + 13

e x p an d \frac{2 x ^{3} + x ^{2} + 5 x - 2}{( x ^{2} + 1 ) ( x ^{2} + 4 )}

e x p an d \frac{1}{4 ( x + 7 )}

e x p an d (- 3 + 3) + (- 33 - 1) i