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

The derivative of (5x)/(sqrt(3x-2)) is (5(3x-4))/(2(3x-2)sqrt(3x-2))

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

The first derivative of (5x)/(sqrt(3x-2)) is (5(3x-4))/(2(3x-2)sqrt(3x-2))

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{2 x ^{4}}{x ^{2} - 2 x} d x

\int_{0}^{1} x 1 + 4 x^{2} d x

\frac{\partial}{\partial x} (x^{2} - 5 x y)

f (x) = x^{1.7}

x \to - 4 lim (\frac{x ^{2} + 9}{x + 2})

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