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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

\frac{2}{3} \cdot \frac{1 \cdot y ^{2} - 2 y \frac{d y}{d x} x}{( y ^{2} ) ^{2}} : \frac{2 ( y - 2 x \frac{d y}{d x} )}{3 y ^{3}}

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

\int_{0}^{L} (3 a x^{2} + 2 b x + c)^{2} d x

\int e^{1 - x} d x

\int 8 x + 5 d x

\frac{d}{d x} (z (x))

\int (\frac{1}{5 - t} + 60 e^{- 0.3 t} + t) d t

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