What is the derivative of (2x^3-2/(3x+4)) ?

The derivative of (2x^3-2/(3x+4)) is (12x^3+24x^2+6)/((3x+4)^2)

What is the first derivative of (2x^3-2/(3x+4)) ?

The first derivative of (2x^3-2/(3x+4)) is (12x^3+24x^2+6)/((3x+4)^2)

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

\frac{12 x ^{3} + 24 x ^{2} + 6}{( 3 x + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (3 x + 4) = 3

= \frac{6 x ^{2} ( 3 x + 4 ) - 3 ( 2 x ^{3} - 2 )}{( 3 x + 4 ) ^{2}}

Expand

6 x^{2} (3 x + 4) - 3 (2 x^{3} - 2) : 12 x^{3} + 24 x^{2} + 6

= \frac{12 x ^{3} + 24 x ^{2} + 6}{( 3 x + 4 ) ^{2}}

x \to - 8 lim (\frac{x ^{2} - 3}{8 - x})

f^{^{'}} (x) = (3 x^{5} - 2)^{20}

\int \frac{8}{1 - cos ( 2 x )} d x

\int \frac{sin ( 2 x )}{4} d x

\int \frac{1}{x ^{\frac{4}{3}}} d x

What is the derivative of (2x^3-2/(3x+4)) ?
The derivative of (2x^3-2/(3x+4)) is (12x^3+24x^2+6)/((3x+4)^2)
What is the first derivative of (2x^3-2/(3x+4)) ?
The first derivative of (2x^3-2/(3x+4)) is (12x^3+24x^2+6)/((3x+4)^2)