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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 x^{4} + 7) = 16 x^{3}

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

= \frac{16 x ^{3} x ^{2} - 2 x ( 4 x ^{4} + 7 )}{( x ^{2} ) ^{2}}

Simplify

\frac{16 x ^{3} x ^{2} - 2 x ( 4 x ^{4} + 7 )}{( x ^{2} ) ^{2}} : \frac{2 ( 4 x ^{4} - 7 )}{x ^{3}}

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

y^{^{'}} = 0.06 y - 0.0006 y^{2}

n = 1 \sum \infty \frac{n ^{3}}{n ^{3}}

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

x \to 0 lim (x csc (3 x))

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

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