What is the derivative of sqrt((5x+1/(4x^2+1))) ?

The derivative of sqrt((5x+1/(4x^2+1))) is (-20x^2-8x+5)/(2sqrt(5x+1)(4x^2+1)^{3/2)}

What is the first derivative of sqrt((5x+1/(4x^2+1))) ?

The first derivative of sqrt((5x+1/(4x^2+1))) is (-20x^2-8x+5)/(2sqrt(5x+1)(4x^2+1)^{3/2)}

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\frac{d}{d x} (\frac{5 x + 1}{4 x ^{2} + 1})

\frac{- 20 x ^{2} - 8 x + 5}{2 5 x + 1 ( 4 x ^{2} + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{5 x + 1}{4 x ^{2} + 1})

Apply the chain rule:

\frac{1}{2 \frac{5 x + 1}{4 x ^{2} + 1}} \frac{d}{d x} (\frac{5 x + 1}{4 x ^{2} + 1})

= \frac{1}{2 \frac{5 x + 1}{4 x ^{2} + 1}} \frac{d}{d x} (\frac{5 x + 1}{4 x ^{2} + 1})

\frac{d}{d x} (\frac{5 x + 1}{4 x ^{2} + 1}) = \frac{- 20 x ^{2} - 8 x + 5}{( 4 x ^{2} + 1 ) ^{2}}

= \frac{1}{2 \frac{5 x + 1}{4 x ^{2} + 1}} \cdot \frac{- 20 x ^{2} - 8 x + 5}{( 4 x ^{2} + 1 ) ^{2}}

Simplify

\frac{1}{2 \frac{5 x + 1}{4 x ^{2} + 1}} \cdot \frac{- 20 x ^{2} - 8 x + 5}{( 4 x ^{2} + 1 ) ^{2}} : \frac{- 20 x ^{2} - 8 x + 5}{2 5 x + 1 ( 4 x ^{2} + 1 ) ^{\frac{3}{2}}}

= \frac{- 20 x ^{2} - 8 x + 5}{2 5 x + 1 ( 4 x ^{2} + 1 ) ^{\frac{3}{2}}}

\frac{d}{d x} (lo g_{6} (5 x + 1))

\frac{d}{d x} ((arcsin (x)) d x)

\int \frac{1}{9 x ^{2} + 18 x + 10} d x

f (x) = \frac{x + 1}{x - 1}

f (x) = (\frac{3 x - 1}{2 x - 3})

What is the derivative of sqrt((5x+1/(4x^2+1))) ?
The derivative of sqrt((5x+1/(4x^2+1))) is (-20x^2-8x+5)/(2sqrt(5x+1)(4x^2+1)^{3/2)}
What is the first derivative of sqrt((5x+1/(4x^2+1))) ?
The first derivative of sqrt((5x+1/(4x^2+1))) is (-20x^2-8x+5)/(2sqrt(5x+1)(4x^2+1)^{3/2)}