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

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

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

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

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\frac{d}{d x} (\frac{3}{x + 3})

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

Solution steps

\frac{d}{d x} (\frac{3}{x + 3})

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 + lim (x^{16 x})

y^{^{'''}} + 2 x \cdot x = 0

\int \frac{x ^{5} + x ^{4} - 8}{x ^{3} - 4 x} d x

\int x^{2} (x + 1)^{2} d x

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

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