What is the derivative of ((6x^2-5)/(4-x))^3 ?

The derivative of ((6x^2-5)/(4-x))^3 is (3(6x^2-5)^2(48x-6x^2-5))/((4-x)^4)

What is the first derivative of ((6x^2-5)/(4-x))^3 ?

The first derivative of ((6x^2-5)/(4-x))^3 is (3(6x^2-5)^2(48x-6x^2-5))/((4-x)^4)

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derivative of

(\frac{6 x ^{2} - 5}{4 - x})^{3}

\frac{3 ( 6 x ^{2} - 5 ) ^{2} ( 48 x - 6 x ^{2} - 5 )}{( 4 - x ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{6 x ^{2} - 5}{4 - x})^{3})

Apply the chain rule:

3 (\frac{6 x ^{2} - 5}{4 - x})^{2} \frac{d}{d x} (\frac{6 x ^{2} - 5}{4 - x})

= 3 (\frac{6 x ^{2} - 5}{4 - x})^{2} \frac{d}{d x} (\frac{6 x ^{2} - 5}{4 - x})

\frac{d}{d x} (\frac{6 x ^{2} - 5}{4 - x}) = \frac{48 x - 6 x ^{2} - 5}{( 4 - x ) ^{2}}

= 3 (\frac{6 x ^{2} - 5}{4 - x})^{2} \frac{48 x - 6 x ^{2} - 5}{( 4 - x ) ^{2}}

Simplify

3 (\frac{6 x ^{2} - 5}{4 - x})^{2} \frac{48 x - 6 x ^{2} - 5}{( 4 - x ) ^{2}} : \frac{3 ( 6 x ^{2} - 5 ) ^{2} ( 48 x - 6 x ^{2} - 5 )}{( 4 - x ) ^{4}}

= \frac{3 ( 6 x ^{2} - 5 ) ^{2} ( 48 x - 6 x ^{2} - 5 )}{( 4 - x ) ^{4}}

x \to 0 lim (\frac{x - 5}{x - 1})

y = (5)^{x}

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

\frac{\partial}{\partial x} (x^{2} z + y, x + y, y + z^{2})

4 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 9 x e^{- y}

What is the derivative of ((6x^2-5)/(4-x))^3 ?
The derivative of ((6x^2-5)/(4-x))^3 is (3(6x^2-5)^2(48x-6x^2-5))/((4-x)^4)
What is the first derivative of ((6x^2-5)/(4-x))^3 ?
The first derivative of ((6x^2-5)/(4-x))^3 is (3(6x^2-5)^2(48x-6x^2-5))/((4-x)^4)