What is the derivative of ((2x^2-1^3)/((5x-8)^2)) ?

The derivative of ((2x^2-1^3)/((5x-8)^2)) is (2(2x^2-1)^2(20x^2-48x+5))/((5x-8)^3)

What is the first derivative of ((2x^2-1^3)/((5x-8)^2)) ?

The first derivative of ((2x^2-1^3)/((5x-8)^2)) is (2(2x^2-1)^2(20x^2-48x+5))/((5x-8)^3)

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\frac{d}{d x} (\frac{( 2 x ^{2} - 1 ) ^{3}}{( 5 x - 8 ) ^{2}})

\frac{2 ( 2 x ^{2} - 1 ) ^{2} ( 20 x ^{2} - 48 x + 5 )}{( 5 x - 8 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{( 2 x ^{2} - 1 ) ^{3}}{( 5 x - 8 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( 2 x ^{2} - 1 ) ^{3} ) ( 5 x - 8 ) ^{2} - \frac{d}{d x} ( ( 5 x - 8 ) ^{2} ) ( 2 x ^{2} - 1 ) ^{3}}{( ( 5 x - 8 ) ^{2} ) ^{2}}

\frac{d}{d x} ((2 x^{2} - 1)^{3}) = 12 x (2 x^{2} - 1)^{2}

\frac{d}{d x} ((5 x - 8)^{2}) = 10 (5 x - 8)

= \frac{12 x ( 2 x ^{2} - 1 ) ^{2} ( 5 x - 8 ) ^{2} - 10 ( 5 x - 8 ) ( 2 x ^{2} - 1 ) ^{3}}{( ( 5 x - 8 ) ^{2} ) ^{2}}

Simplify

\frac{12 x ( 2 x ^{2} - 1 ) ^{2} ( 5 x - 8 ) ^{2} - 10 ( 5 x - 8 ) ( 2 x ^{2} - 1 ) ^{3}}{( ( 5 x - 8 ) ^{2} ) ^{2}} : \frac{2 ( 2 x ^{2} - 1 ) ^{2} ( 20 x ^{2} - 48 x + 5 )}{( 5 x - 8 ) ^{3}}

= \frac{2 ( 2 x ^{2} - 1 ) ^{2} ( 20 x ^{2} - 48 x + 5 )}{( 5 x - 8 ) ^{3}}

\int t^{2} + 1 d t

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

\frac{d}{d t} (8)

\int \frac{e ^{\frac{7}{x}}}{x ^{2}} d x

x \to 0 lim (\frac{x - ∣ x ∣}{x})

What is the derivative of ((2x^2-1^3)/((5x-8)^2)) ?
The derivative of ((2x^2-1^3)/((5x-8)^2)) is (2(2x^2-1)^2(20x^2-48x+5))/((5x-8)^3)
What is the first derivative of ((2x^2-1^3)/((5x-8)^2)) ?
The first derivative of ((2x^2-1^3)/((5x-8)^2)) is (2(2x^2-1)^2(20x^2-48x+5))/((5x-8)^3)