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

The derivative of In((sqrt(4+x^2)/x)) is -(4nI)/(x^2sqrt(4+x^2))

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

The first derivative of In((sqrt(4+x^2)/x)) is -(4nI)/(x^2sqrt(4+x^2))

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

- \frac{4 n I}{x ^{2} 4 + x ^{2}}

Solution steps

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

Treat

n, I

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

= I n \frac{\frac{x}{4 + x ^{2}} x - 1 \cdot 4 + x ^{2}}{x ^{2}}

Simplify

I n \frac{\frac{x}{4 + x ^{2}} x - 1 \cdot 4 + x ^{2}}{x ^{2}} : - \frac{4 n I}{x ^{2} 4 + x ^{2}}

= - \frac{4 n I}{x ^{2} 4 + x ^{2}}

\int \frac{sin ( 5 x )}{cos ( 5 x )} d x

6 x, 4 x^{2}

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

\frac{d y}{d x} = y, y (0) = 1

\frac{d y}{d x} = 8 x^{4} (6 + y^{2})^{\frac{3}{2}}

What is the derivative of In((sqrt(4+x^2)/x)) ?
The derivative of In((sqrt(4+x^2)/x)) is -(4nI)/(x^2sqrt(4+x^2))
What is the first derivative of In((sqrt(4+x^2)/x)) ?
The first derivative of In((sqrt(4+x^2)/x)) is -(4nI)/(x^2sqrt(4+x^2))