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Popular Calculus >

derivative of x^{2/3}+y^{2/3}

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

derivative of-tan(x^2)

\frac{d}{d x} (- tan (x^{2}))

integral of 1/(ln(x^2))

\int \frac{1}{ln ( x ^{2} )} d x

sum from n=1 to infinity of (3^n)/(5^n)

n = 1 \sum \infty \frac{3 ^{n}}{5 ^{n}}

limit as x approaches 0 of (9+x)/(x^3)

x \to 0 lim (\frac{9 + x}{x ^{3}})

(\partial)/(\partial x)((2x^2-5x)^3(2x+1))

\frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3} (2 x + 1))

Frequently Asked Questions (FAQ)

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