What is the derivative of (4x/(sqrt(x^2+1))) ?

The derivative of (4x/(sqrt(x^2+1))) is 4/((x^2+1)sqrt(x^2+1))

What is the first derivative of (4x/(sqrt(x^2+1))) ?

The first derivative of (4x/(sqrt(x^2+1))) is 4/((x^2+1)sqrt(x^2+1))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d s} (\frac{s}{s ^{2} + 25})

\int (4 x + 3)^{7} d x

\int 6 x^{2} (1 - x) d x

\int \frac{17}{17 + e ^{x}} d x

What is the derivative of (4x/(sqrt(x^2+1))) ?
The derivative of (4x/(sqrt(x^2+1))) is 4/((x^2+1)sqrt(x^2+1))
What is the first derivative of (4x/(sqrt(x^2+1))) ?
The first derivative of (4x/(sqrt(x^2+1))) is 4/((x^2+1)sqrt(x^2+1))