What is the derivative of sqrt((3x+1/(5x^2+1))) ?

The derivative of sqrt((3x+1/(5x^2+1))) is (-15x^2-10x+3)/(2sqrt(3x+1)(5x^2+1)^{3/2)}

What is the first derivative of sqrt((3x+1/(5x^2+1))) ?

The first derivative of sqrt((3x+1/(5x^2+1))) is (-15x^2-10x+3)/(2sqrt(3x+1)(5x^2+1)^{3/2)}

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\frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

\frac{- 15 x ^{2} - 10 x + 3}{2 3 x + 1 ( 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

Apply the chain rule:

\frac{1}{2 \frac{3 x + 1}{5 x ^{2} + 1}} \frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

= \frac{1}{2 \frac{3 x + 1}{5 x ^{2} + 1}} \frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

\frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1}) = \frac{- 15 x ^{2} - 10 x + 3}{( 5 x ^{2} + 1 ) ^{2}}

= \frac{1}{2 \frac{3 x + 1}{5 x ^{2} + 1}} \cdot \frac{- 15 x ^{2} - 10 x + 3}{( 5 x ^{2} + 1 ) ^{2}}

Simplify

\frac{1}{2 \frac{3 x + 1}{5 x ^{2} + 1}} \cdot \frac{- 15 x ^{2} - 10 x + 3}{( 5 x ^{2} + 1 ) ^{2}} : \frac{- 15 x ^{2} - 10 x + 3}{2 3 x + 1 ( 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

= \frac{- 15 x ^{2} - 10 x + 3}{2 3 x + 1 ( 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

f (x) = \frac{sin ( x )}{x ^{3}}

x y^{^{'}} + y = 6 x^{2}, y (1) = 2

n \to \infty lim (n^{10})

f (x) = 2 x - x ln ∣ x ∣

n = 0 \sum \infty \frac{1 ^{n}}{2 n + 1}

What is the derivative of sqrt((3x+1/(5x^2+1))) ?
The derivative of sqrt((3x+1/(5x^2+1))) is (-15x^2-10x+3)/(2sqrt(3x+1)(5x^2+1)^{3/2)}
What is the first derivative of sqrt((3x+1/(5x^2+1))) ?
The first derivative of sqrt((3x+1/(5x^2+1))) is (-15x^2-10x+3)/(2sqrt(3x+1)(5x^2+1)^{3/2)}