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

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

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

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

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derivative of

\frac{3}{x + 4}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

ln (x - 3)

f (t) = 2 e^{- t} cos (2 π t) - 1

\int 2 1 - x^{2} d x

\frac{d y}{d x}, e^{(\frac{x}{y})} = 6 x - y

(x - 2) (x^{2} - 10 x + 25)

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