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

The derivative of sqrt((x^3/(2-x))) is (sqrt(x)(-x+3))/((-x+2)^{3/2)}

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

The first derivative of sqrt((x^3/(2-x))) is (sqrt(x)(-x+3))/((-x+2)^{3/2)}

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{3}}{2 - x}) = \frac{6 x ^{2} - 2 x ^{3}}{( 2 - x ) ^{2}}

= \frac{1}{2 \frac{x ^{3}}{2 - x}} \cdot \frac{6 x ^{2} - 2 x ^{3}}{( 2 - x ) ^{2}}

Simplify

\frac{1}{2 \frac{x ^{3}}{2 - x}} \cdot \frac{6 x ^{2} - 2 x ^{3}}{( 2 - x ) ^{2}} : \frac{x ( - x + 3 )}{( - x + 2 ) ^{\frac{3}{2}}}

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

\frac{d y}{d x} = 0.276 y - 0.0012 y^{2}

\int \frac{x}{x ^{8} - 1} d x

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

y^{^{''}} + 9 y^{^{'}} + 18 y = 2050 e^{2 t} cos (10 t)

\int_{- 3}^{1} x + 3 d x

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