What is the derivative of (4x^3/(x^4+27)) ?

The derivative of (4x^3/(x^4+27)) is (4(-x^6+81x^2))/((x^4+27)^2)

What is the first derivative of (4x^3/(x^4+27)) ?

The first derivative of (4x^3/(x^4+27)) is (4(-x^6+81x^2))/((x^4+27)^2)

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\frac{d}{d x} (\frac{4 x ^{3}}{x ^{4} + 27})

\frac{4 ( - x ^{6} + 81 x ^{2} )}{( x ^{4} + 27 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{3}}{x ^{4} + 27})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{x ^{3}}{x ^{4} + 27})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d}{d x} ( x ^{3} ) ( x ^{4} + 27 ) - \frac{d}{d x} ( x ^{4} + 27 ) x ^{3}}{( x ^{4} + 27 ) ^{2}}

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

\frac{d}{d x} (x^{4} + 27) = 4 x^{3}

= 4 \cdot \frac{3 x ^{2} ( x ^{4} + 27 ) - 4 x ^{3} x ^{3}}{( x ^{4} + 27 ) ^{2}}

Simplify

4 \cdot \frac{3 x ^{2} ( x ^{4} + 27 ) - 4 x ^{3} x ^{3}}{( x ^{4} + 27 ) ^{2}} : \frac{4 ( - x ^{6} + 81 x ^{2} )}{( x ^{4} + 27 ) ^{2}}

= \frac{4 ( - x ^{6} + 81 x ^{2} )}{( x ^{4} + 27 ) ^{2}}

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

\frac{\partial}{\partial x} (ln (x^{8} y))

x \to 0 lim (- \frac{1}{x ^{2}})

\frac{d}{d x} (3 sin^{2} (2 x))

\int \frac{sin ^{2} ( x )}{1 + cos ^{2} ( x )} d x

What is the derivative of (4x^3/(x^4+27)) ?
The derivative of (4x^3/(x^4+27)) is (4(-x^6+81x^2))/((x^4+27)^2)
What is the first derivative of (4x^3/(x^4+27)) ?
The first derivative of (4x^3/(x^4+27)) is (4(-x^6+81x^2))/((x^4+27)^2)