derivative of 3(x^2+y^2^2)

解答

\frac{d}{d x} (3 (x^{2} + y^{2})^{2})

6 (x^{2} + y^{2}) (2 x + 2 y \frac{d y}{d x})

求解步骤

\frac{d}{d x} (3 (x^{2} + y^{2})^{2})

将常数提出:

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

= 3 \frac{d}{d x} ((x^{2} + y^{2})^{2})

使用连锁律:

2 (x^{2} + y^{2}) \frac{d}{d x} (x^{2} + y^{2})

= 2 (x^{2} + y^{2}) \frac{d}{d x} (x^{2} + y^{2})

\frac{d}{d x} (x^{2} + y^{2}) = 2 x + 2 y \frac{d y}{d x}

= 3 \cdot 2 (x^{2} + y^{2}) (2 x + 2 y \frac{d y}{d x})

化简

= 6 (x^{2} + y^{2}) (2 x + 2 y \frac{d y}{d x})

d er i v a t i v e y = 4 cot (3 - 2 x)

\int_{0}^{2} (4 x - 2 x^{2}) d x

\frac{d y}{d x} y = (x^{2} + 3 x)^{2}

x \to - \infty lim (\frac{4}{x})

\int \frac{cos ( x )}{sin ^{2} ( x ) - 4} d x