What is the derivative of sqrt((5x^3)/(2x-2)) ?

The derivative of sqrt((5x^3)/(2x-2)) is (sqrt(5)x^{3/2}(2x-3)sqrt(2x-2))/(4sqrt(x^2)(x-1)^2)

What is the first derivative of sqrt((5x^3)/(2x-2)) ?

The first derivative of sqrt((5x^3)/(2x-2)) is (sqrt(5)x^{3/2}(2x-3)sqrt(2x-2))/(4sqrt(x^2)(x-1)^2)

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derivative of

\frac{5 x ^{3}}{2 x - 2}

\frac{5 x ^{\frac{3}{2}} ( 2 x - 3 ) 2 x - 2}{4 x ^{2} ( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x ^{3}}{2 x - 2})

Apply the chain rule:

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

= \frac{1}{2 \frac{5 x ^{3}}{2 x - 2}} \frac{d}{d x} (\frac{5 x ^{3}}{2 x - 2})

\frac{d}{d x} (\frac{5 x ^{3}}{2 x - 2}) = \frac{5 x ^{2} ( 2 x - 3 )}{2 ( x - 1 ) ^{2}}

= \frac{1}{2 \frac{5 x ^{3}}{2 x - 2}} \cdot \frac{5 x ^{2} ( 2 x - 3 )}{2 ( x - 1 ) ^{2}}

Simplify

\frac{1}{2 \frac{5 x ^{3}}{2 x - 2}} \cdot \frac{5 x ^{2} ( 2 x - 3 )}{2 ( x - 1 ) ^{2}} : \frac{5 x ^{\frac{3}{2}} ( 2 x - 3 ) 2 x - 2}{4 x ^{2} ( x - 1 ) ^{2}}

= \frac{5 x ^{\frac{3}{2}} ( 2 x - 3 ) 2 x - 2}{4 x ^{2} ( x - 1 ) ^{2}}

y^{^{''}} - y^{^{'}} - 12 y = 2 e^{3 x}

\frac{\partial}{\partial v} (u (v) (v)^{2} e^{- v})

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x \to - 7 lim (\frac{x + 7}{∣ x + 7 ∣})

\int_{1}^{e} ln (10 x) d x

What is the derivative of sqrt((5x^3)/(2x-2)) ?
The derivative of sqrt((5x^3)/(2x-2)) is (sqrt(5)x^{3/2}(2x-3)sqrt(2x-2))/(4sqrt(x^2)(x-1)^2)
What is the first derivative of sqrt((5x^3)/(2x-2)) ?
The first derivative of sqrt((5x^3)/(2x-2)) is (sqrt(5)x^{3/2}(2x-3)sqrt(2x-2))/(4sqrt(x^2)(x-1)^2)