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受欢迎的微积分 >

(\partial)/(\partial x)(xy^2z^3)

解答

\frac{\partial}{\partial x} (x \cdot y^{2} \cdot z^{3})

解答

y^{2} z^{3}

求解步骤

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

将

y, z

视为常数

将常数提出:

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

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

使用常见微分定则:

\frac{\partial}{\partial x} (x) = 1

= y^{2} z^{3} \cdot 1

化简

= y^{2} z^{3}

流行的例子

展开 (4x-3)^5(3-x^3)^2

e x p an d (4 x - 3)^{5} (3 - x^{3})^{2}

y^{''}-16y^'+64y=t^{-2}e^{8t}

y^{^{''}} - 16 y^{^{'}} + 64 y = t^{- 2} e^{8 t}

tangent f(x)=sqrt(5x+75),\at x=5

t an g e n t f (x) = 5 x + 75, at x = 5

integral of (1+2x)/(1+x^2)

\int \frac{1 + 2 x}{1 + x ^{2}} d x

integral of 1/(sqrt((1+x^2)))

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