What is the derivative of (5x^2)/(3x-1) ?

The derivative of (5x^2)/(3x-1) is (5(3x^2-2x))/((3x-1)^2)

What is the first derivative of (5x^2)/(3x-1) ?

The first derivative of (5x^2)/(3x-1) is (5(3x^2-2x))/((3x-1)^2)

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derivative of

\frac{5 x ^{2}}{3 x - 1}

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int_{1}^{2} 3 - \frac{6}{x ^{2}} d x

\int \frac{6 cosh ( x )}{x} d x

y^{^{'''}} + 4 y^{^{''}} - 16 y^{^{'}} - 64 y = 0

\frac{d}{d x} (5 cos (x) - cos (5 x))

\int \frac{3 x ^{2} - x + 1}{x ^{3} - x ^{2}} d x

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