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

The derivative of (((3x^2)/(2x+4))^3) is (81x^5(x+4))/(2(2x+4)^2(x+2)^2)

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

The first derivative of (((3x^2)/(2x+4))^3) is (81x^5(x+4))/(2(2x+4)^2(x+2)^2)

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

\frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{3 x ^{2}}{2 x + 4})^{2} \frac{3 x ( x + 4 )}{2 ( x + 2 ) ^{2}} : \frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

= \frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

x \to 0 lim (\frac{3}{x} + \frac{3}{x ^{2} - x})

\frac{d}{d x} (2 x + sin (x))

\frac{d}{d x} (\frac{x ^{2} cos ( x )}{tan ( x )})

\int (z + 1) e^{z} d z

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

What is the derivative of (((3x^2)/(2x+4))^3) ?
The derivative of (((3x^2)/(2x+4))^3) is (81x^5(x+4))/(2(2x+4)^2(x+2)^2)
What is the first derivative of (((3x^2)/(2x+4))^3) ?
The first derivative of (((3x^2)/(2x+4))^3) is (81x^5(x+4))/(2(2x+4)^2(x+2)^2)