What is the derivative of sqrt(2x^2+2y^2) ?

The derivative of sqrt(2x^2+2y^2) is (2(x+y\frac{dy)/(dx))}{sqrt(2x^2+2y^2)}

What is the first derivative of sqrt(2x^2+2y^2) ?

The first derivative of sqrt(2x^2+2y^2) is (2(x+y\frac{dy)/(dx))}{sqrt(2x^2+2y^2)}

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\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}}

Solution steps

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

Apply the chain rule:

\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})

Simplify

\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

What is the derivative of sqrt(2x^2+2y^2) ?
The derivative of sqrt(2x^2+2y^2) is (2(x+y\frac{dy)/(dx))}{sqrt(2x^2+2y^2)}
What is the first derivative of sqrt(2x^2+2y^2) ?
The first derivative of sqrt(2x^2+2y^2) is (2(x+y\frac{dy)/(dx))}{sqrt(2x^2+2y^2)}