What is the derivative of f(x)=(4(x^2-1))/((4x^3-2x)^{2/3)} ?

The derivative of f(x)=(4(x^2-1))/((4x^3-2x)^{2/3)} is (4(16x^2-4))/(3(4x^3-2x)^{5/3)}

What is the first derivative of f(x)=(4(x^2-1))/((4x^3-2x)^{2/3)} ?

The first derivative of f(x)=(4(x^2-1))/((4x^3-2x)^{2/3)} is (4(16x^2-4))/(3(4x^3-2x)^{5/3)}

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derivative of

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

\frac{4 ( 16 x ^{2} - 4 )}{3 ( 4 x ^{3} - 2 x ) ^{\frac{5}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((4 x^{3} - 2 x)^{\frac{2}{3}}) = \frac{2 ( 12 x ^{2} - 2 )}{3 ( 4 x ^{3} - 2 x ) ^{\frac{1}{3}}}

= 4 \cdot \frac{2 x ( 4 x ^{3} - 2 x ) ^{\frac{2}{3}} - \frac{2 ( 12 x ^{2} - 2 )}{3 ( 4 x ^{3} - 2 x ) ^{\frac{1}{3}}} ( x ^{2} - 1 )}{( ( 4 x ^{3} - 2 x ) ^{\frac{2}{3}} ) ^{2}}

Simplify

4 \cdot \frac{2 x ( 4 x ^{3} - 2 x ) ^{\frac{2}{3}} - \frac{2 ( 12 x ^{2} - 2 )}{3 ( 4 x ^{3} - 2 x ) ^{\frac{1}{3}}} ( x ^{2} - 1 )}{( ( 4 x ^{3} - 2 x ) ^{\frac{2}{3}} ) ^{2}} : \frac{4 ( 16 x ^{2} - 4 )}{3 ( 4 x ^{3} - 2 x ) ^{\frac{5}{3}}}

= \frac{4 ( 16 x ^{2} - 4 )}{3 ( 4 x ^{3} - 2 x ) ^{\frac{5}{3}}}

\int t e^{- t^{2}} d t

x \to - \frac{π}{9} lim (9 x^{2} (5 x))

ln (8 - t^{2})

\int cot^{6} (x) csc^{2} (x) d x

\int \frac{1}{x ^{0.5}} d x

What is the derivative of f(x)=(4(x^2-1))/((4x^3-2x)^{2/3)} ?
The derivative of f(x)=(4(x^2-1))/((4x^3-2x)^{2/3)} is (4(16x^2-4))/(3(4x^3-2x)^{5/3)}
What is the first derivative of f(x)=(4(x^2-1))/((4x^3-2x)^{2/3)} ?
The first derivative of f(x)=(4(x^2-1))/((4x^3-2x)^{2/3)} is (4(16x^2-4))/(3(4x^3-2x)^{5/3)}