What is the derivative of (4+sqrt(x)/(4-sqrt(x))) ?

The derivative of (4+sqrt(x)/(4-sqrt(x))) is 4/(sqrt(x)(4-\sqrt{x))^2}

What is the first derivative of (4+sqrt(x)/(4-sqrt(x))) ?

The first derivative of (4+sqrt(x)/(4-sqrt(x))) is 4/(sqrt(x)(4-\sqrt{x))^2}

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\frac{d}{d x} (\frac{4 + x}{4 - x})

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

Solution steps

\frac{d}{d x} (\frac{4 + x}{4 - x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 + x) = \frac{1}{2 x}

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

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

Simplify

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

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

y^{^{''}} + 4 y = - 12 sin (2 t)

e^{\frac{1}{x}}

ln (4 - x^{2})

x \to 2 lim (\frac{3}{∣ x - 2 ∣})

y d x + (- 2 x - 2 y) d y = 0

What is the derivative of (4+sqrt(x)/(4-sqrt(x))) ?
The derivative of (4+sqrt(x)/(4-sqrt(x))) is 4/(sqrt(x)(4-\sqrt{x))^2}
What is the first derivative of (4+sqrt(x)/(4-sqrt(x))) ?
The first derivative of (4+sqrt(x)/(4-sqrt(x))) is 4/(sqrt(x)(4-\sqrt{x))^2}