What is the derivative of 1/(6x-12)sqrt(2x+16) ?

The derivative of 1/(6x-12)sqrt(2x+16) is (-x-18)/(6(x-2)^2sqrt(2x+16))

What is the first derivative of 1/(6x-12)sqrt(2x+16) ?

The first derivative of 1/(6x-12)sqrt(2x+16) is (-x-18)/(6(x-2)^2sqrt(2x+16))

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derivative of

\frac{1}{6 x - 12} 2 x + 16

\frac{- x - 18}{6 ( x - 2 ) ^{2} 2 x + 16}

Solution steps

\frac{d}{d x} (\frac{1}{6 x - 12} 2 x + 16)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{6 x - 12}, g = 2 x + 16

= \frac{d}{d x} (\frac{1}{6 x - 12}) 2 x + 16 + \frac{d}{d x} (2 x + 16) \frac{1}{6 x - 12}

\frac{d}{d x} (\frac{1}{6 x - 12}) = - \frac{1}{6 ( x - 2 ) ^{2}}

\frac{d}{d x} (2 x + 16) = \frac{1}{2 x + 16}

= (- \frac{1}{6 ( x - 2 ) ^{2}}) 2 x + 16 + \frac{1}{2 x + 16} \cdot \frac{1}{6 x - 12}

Simplify

(- \frac{1}{6 ( x - 2 ) ^{2}}) 2 x + 16 + \frac{1}{2 x + 16} \cdot \frac{1}{6 x - 12} : \frac{- x - 18}{6 ( x - 2 ) ^{2} 2 x + 16}

= \frac{- x - 18}{6 ( x - 2 ) ^{2} 2 x + 16}

\frac{d}{d x} (x + \frac{1}{x ^{3}})

\frac{\partial}{\partial x} (x^{2} + y^{3})

h (x) = 3 e^{x} - 7 x, (0, 3)

\frac{1}{2 s + 5}

x \to + 0 lim (cos^{2} (x))

What is the derivative of 1/(6x-12)sqrt(2x+16) ?
The derivative of 1/(6x-12)sqrt(2x+16) is (-x-18)/(6(x-2)^2sqrt(2x+16))
What is the first derivative of 1/(6x-12)sqrt(2x+16) ?
The first derivative of 1/(6x-12)sqrt(2x+16) is (-x-18)/(6(x-2)^2sqrt(2x+16))