What is the derivative of f(x)= 3/(2x+5) ?

The derivative of f(x)= 3/(2x+5) is -6/((2x+5)^2)

What is the first derivative of f(x)= 3/(2x+5) ?

The first derivative of f(x)= 3/(2x+5) is -6/((2x+5)^2)

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derivative of

f (x) = \frac{3}{2 x + 5}

- \frac{6}{( 2 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3}{2 x + 5})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{1}{2 x + 5})

Apply exponent rule:

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

= 3 \frac{d}{d x} ((2 x + 5)^{- 1})

Apply the chain rule:

- \frac{1}{( 2 x + 5 ) ^{2}} \frac{d}{d x} (2 x + 5)

= - \frac{1}{( 2 x + 5 ) ^{2}} \frac{d}{d x} (2 x + 5)

\frac{d}{d x} (2 x + 5) = 2

= 3 (- \frac{1}{( 2 x + 5 ) ^{2}} \cdot 2)

Simplify

3 (- \frac{1}{( 2 x + 5 ) ^{2}} \cdot 2) : - \frac{6}{( 2 x + 5 ) ^{2}}

= - \frac{6}{( 2 x + 5 ) ^{2}}

y^{^{'}} = 2 y + sin (2 t)

\frac{\partial}{\partial x} (e^{- (x^{3} + y^{3})})

\frac{\partial}{\partial x} (x^{3} + y^{3} - 5 x y)

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

f (x) = x^{3} - 5 x + 3, at x = 3

What is the derivative of f(x)= 3/(2x+5) ?
The derivative of f(x)= 3/(2x+5) is -6/((2x+5)^2)
What is the first derivative of f(x)= 3/(2x+5) ?
The first derivative of f(x)= 3/(2x+5) is -6/((2x+5)^2)