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

The derivative of f(x)= 3/(x+3) is -3/((x+3)^2)

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

The first derivative of f(x)= 3/(x+3) is -3/((x+3)^2)

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derivative of

f (x) = \frac{3}{x + 3}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int cos (5 x) cos (7 x) d x

\int_{0}^{3} - x^{2} + 9 d x

y^{^{'}} = \frac{( y ^{2} - 1 )}{2 x}, y (1) = - 2

\frac{d y}{d t} = - \frac{3 y}{t} - 2 - t^{- 4}, y (1) = 4

x \to 2 lim (x)

What is the derivative of f(x)= 3/(x+3) ?
The derivative of f(x)= 3/(x+3) is -3/((x+3)^2)
What is the first derivative of f(x)= 3/(x+3) ?
The first derivative of f(x)= 3/(x+3) is -3/((x+3)^2)