What is the derivative of sqrt((2x)/(6x-5)) ?

The derivative of sqrt((2x)/(6x-5)) is -5/(sqrt(2)\sqrt{x)(6x-5)^{3/2}}

What is the first derivative of sqrt((2x)/(6x-5)) ?

The first derivative of sqrt((2x)/(6x-5)) is -5/(sqrt(2)\sqrt{x)(6x-5)^{3/2}}

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derivative of

\frac{2 x}{6 x - 5}

- \frac{5}{2 x ( 6 x - 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{2 x}{6 x - 5})

Apply the chain rule:

\frac{1}{2 \frac{2 x}{6 x - 5}} \frac{d}{d x} (\frac{2 x}{6 x - 5})

= \frac{1}{2 \frac{2 x}{6 x - 5}} \frac{d}{d x} (\frac{2 x}{6 x - 5})

\frac{d}{d x} (\frac{2 x}{6 x - 5}) = - \frac{10}{( 6 x - 5 ) ^{2}}

= \frac{1}{2 \frac{2 x}{6 x - 5}} (- \frac{10}{( 6 x - 5 ) ^{2}})

Simplify

\frac{1}{2 \frac{2 x}{6 x - 5}} (- \frac{10}{( 6 x - 5 ) ^{2}}) : - \frac{5}{2 x ( 6 x - 5 ) ^{\frac{3}{2}}}

= - \frac{5}{2 x ( 6 x - 5 ) ^{\frac{3}{2}}}

x \to 0 lim (e^{- x^{2}})

\frac{d y}{d x} = \frac{x - 1}{y - 3}

y = \frac{5}{3}, y = \frac{1}{4 - x ^{2}}

\frac{d}{d t} (2 + t)

\int 2 x^{3} + 3 x d x

What is the derivative of sqrt((2x)/(6x-5)) ?
The derivative of sqrt((2x)/(6x-5)) is -5/(sqrt(2)\sqrt{x)(6x-5)^{3/2}}
What is the first derivative of sqrt((2x)/(6x-5)) ?
The first derivative of sqrt((2x)/(6x-5)) is -5/(sqrt(2)\sqrt{x)(6x-5)^{3/2}}