What is the derivative of 4/(x+6) ?

The derivative of 4/(x+6) is -4/((x+6)^2)

What is the first derivative of 4/(x+6) ?

The first derivative of 4/(x+6) is -4/((x+6)^2)

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\frac{d}{d x} (\frac{4}{x + 6})

- \frac{4}{( x + 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{x + 6})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{x + 6})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((x + 6)^{- 1})

Apply the chain rule:

- \frac{1}{( x + 6 ) ^{2}} \frac{d}{d x} (x + 6)

= - \frac{1}{( x + 6 ) ^{2}} \frac{d}{d x} (x + 6)

\frac{d}{d x} (x + 6) = 1

= 4 (- \frac{1}{( x + 6 ) ^{2}} \cdot 1)

Simplify

4 (- \frac{1}{( x + 6 ) ^{2}} \cdot 1) : - \frac{4}{( x + 6 ) ^{2}}

= - \frac{4}{( x + 6 ) ^{2}}

f (x) = - 4 tan (x) - 1, at x = - \frac{π}{4}

\frac{\partial}{\partial x} (2 y^{6} + 4 y^{8} x^{3})

- \frac{9}{x}

f (x) = x^{3} - 3 x + 1, (3, 19)

\int cos^{15} (x) sin (x) d x

What is the derivative of 4/(x+6) ?
The derivative of 4/(x+6) is -4/((x+6)^2)
What is the first derivative of 4/(x+6) ?
The first derivative of 4/(x+6) is -4/((x+6)^2)