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

解答

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

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

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (2 x^{2} + 2 y^{2}) = 4 x + 4 y \frac{d y}{d x}

= \frac{1}{2 2 x ^{2} + 2 y ^{2}} (4 x + 4 y \frac{d y}{d x})

化简

\frac{1}{2 2 x ^{2} + 2 y ^{2}} (4 x + 4 y \frac{d y}{d x}) : \frac{2 ( x + y \frac{d y}{d x} )}{2 x ^{2} + 2 y ^{2}}

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

\int_{- 2}^{4} 10 + 4 x - 3 x^{3} d x

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

\int \frac{5 x + 1}{6 x ^{2} + 7 x - 3} d x

\int sin (x) + 1 d x

\int \frac{1}{( 4 x ^{2} + 9 ) ^{\frac{3}{2}}} d x