What is the derivative of (sqrt(x^2+4x+3)/(sqrt(x))) ?

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

What is the first derivative of (sqrt(x^2+4x+3)/(sqrt(x))) ?

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

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\frac{d}{d x} (\frac{x ^{2} + 4 x + 3}{x})

\frac{x ^{2} - 3}{2 x ^{\frac{3}{2}} x ^{2} + 4 x + 3}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 4 x + 3}{x})

Simplify

\frac{x ^{2} + 4 x + 3}{x} : \frac{x ^{2} + 4 x + 3}{x}

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

Apply the chain rule:

\frac{1}{2 \frac{x ^{2} + 4 x + 3}{x}} \frac{d}{d x} (\frac{x ^{2} + 4 x + 3}{x})

= \frac{1}{2 \frac{x ^{2} + 4 x + 3}{x}} \frac{d}{d x} (\frac{x ^{2} + 4 x + 3}{x})

\frac{d}{d x} (\frac{x ^{2} + 4 x + 3}{x}) = \frac{x ^{2} - 3}{x ^{2}}

= \frac{1}{2 \frac{x ^{2} + 4 x + 3}{x}} \cdot \frac{x ^{2} - 3}{x ^{2}}

Simplify

\frac{1}{2 \frac{x ^{2} + 4 x + 3}{x}} \cdot \frac{x ^{2} - 3}{x ^{2}} : \frac{x ^{2} - 3}{2 x ^{\frac{3}{2}} x ^{2} + 4 x + 3}

= \frac{x ^{2} - 3}{2 x ^{\frac{3}{2}} x ^{2} + 4 x + 3}

\frac{d}{d x} (x^{4} (tan (x) + sec (x)))

x \to 0 lim (- x^{2} + 5 x + a)

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

\frac{d}{d t} (t^{2} (3 - t)^{3})

\frac{\partial}{\partial x} (tan (\frac{x}{y}))

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