What is the derivative of ((2x^2-4))/((3x^2+7)) ?

The derivative of ((2x^2-4))/((3x^2+7)) is (52x)/((3x^2+7)^2)

What is the first derivative of ((2x^2-4))/((3x^2+7)) ?

The first derivative of ((2x^2-4))/((3x^2+7)) is (52x)/((3x^2+7)^2)

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derivative of

\frac{( 2 x ^{2} - 4 )}{( 3 x ^{2} + 7 )}

\frac{52 x}{( 3 x ^{2} + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{2} - 4}{3 x ^{2} + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} - 4 ) ( 3 x ^{2} + 7 ) - \frac{d}{d x} ( 3 x ^{2} + 7 ) ( 2 x ^{2} - 4 )}{( 3 x ^{2} + 7 ) ^{2}}

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

\frac{d}{d x} (3 x^{2} + 7) = 6 x

= \frac{4 x ( 3 x ^{2} + 7 ) - 6 x ( 2 x ^{2} - 4 )}{( 3 x ^{2} + 7 ) ^{2}}

Expand

4 x (3 x^{2} + 7) - 6 x (2 x^{2} - 4) : 52 x

= \frac{52 x}{( 3 x ^{2} + 7 ) ^{2}}

\frac{t ^{3}}{6}

\frac{1}{x ^{2} + y ^{2}}

y = x^{5} + x^{3} - x + 10

4 x^{2} - 5 x - 1

\frac{11}{x ^{4}}

What is the derivative of ((2x^2-4))/((3x^2+7)) ?
The derivative of ((2x^2-4))/((3x^2+7)) is (52x)/((3x^2+7)^2)
What is the first derivative of ((2x^2-4))/((3x^2+7)) ?
The first derivative of ((2x^2-4))/((3x^2+7)) is (52x)/((3x^2+7)^2)