What is the derivative of (x^2+y^2^3) ?

The derivative of (x^2+y^2^3) is 3(x^2+y^2)^2(2x+2y(dy)/(dx))

What is the first derivative of (x^2+y^2^3) ?

The first derivative of (x^2+y^2^3) is 3(x^2+y^2)^2(2x+2y(dy)/(dx))

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

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

Solution steps

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

Apply the chain rule:

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

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

What is the derivative of (x^2+y^2^3) ?
The derivative of (x^2+y^2^3) is 3(x^2+y^2)^2(2x+2y(dy)/(dx))
What is the first derivative of (x^2+y^2^3) ?
The first derivative of (x^2+y^2^3) is 3(x^2+y^2)^2(2x+2y(dy)/(dx))