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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

= \frac{1 \cdot ( x - 4 ) ^{2} - 2 ( x - 4 ) x}{( ( x - 4 ) ^{2} ) ^{2}}

Simplify

\frac{1 \cdot ( x - 4 ) ^{2} - 2 ( x - 4 ) x}{( ( x - 4 ) ^{2} ) ^{2}} : \frac{- 4 - x}{( x - 4 ) ^{3}}

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

3 x, \frac{1}{3} x, 0, 4

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

\int_{1}^{3} 11 r^{3} ln (r) d r

y^{^{''}} + 25 y = 40 sin (5 t)

\frac{\partial}{\partial y} (x y + y)

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