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

The derivative of (x^2+y^2^{2/3}) is (2(2x+2y\frac{dy)/(dx))}{3(x^2+y^2)^{1/3}}

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

The first derivative of (x^2+y^2^{2/3}) is (2(2x+2y\frac{dy)/(dx))}{3(x^2+y^2)^{1/3}}

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

\frac{2 ( 2 x + 2 y \frac{d y}{d x} )}{3 ( x ^{2} + y ^{2} ) ^{\frac{1}{3}}}

Solution steps

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

Apply the chain rule:

\frac{2}{3 ( x ^{2} + y ^{2} ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} + y^{2})

= \frac{2}{3 ( x ^{2} + y ^{2} ) ^{\frac{1}{3}}} \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}

= \frac{2}{3 ( x ^{2} + y ^{2} ) ^{\frac{1}{3}}} (2 x + 2 y \frac{d y}{d x})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 ( 2 x + 2 y \frac{d y}{d x} )}{3 ( x ^{2} + y ^{2} ) ^{\frac{1}{3}}}

f (x) = ln (x^{3} + 5 x + 3)

(2 x + 3) \frac{d y}{d x} = y + (2 x + 3)^{\frac{1}{2}}

y = - \frac{4}{5 x ^{5}} + \frac{15}{4 x ^{4}}

f (x) = x^{2} + 21

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

What is the derivative of (x^2+y^2^{2/3}) ?
The derivative of (x^2+y^2^{2/3}) is (2(2x+2y\frac{dy)/(dx))}{3(x^2+y^2)^{1/3}}
What is the first derivative of (x^2+y^2^{2/3}) ?
The first derivative of (x^2+y^2^{2/3}) is (2(2x+2y\frac{dy)/(dx))}{3(x^2+y^2)^{1/3}}