What is the derivative of f(x)= 4/(5x+1) ?

The derivative of f(x)= 4/(5x+1) is -(20)/((5x+1)^2)

What is the first derivative of f(x)= 4/(5x+1) ?

The first derivative of f(x)= 4/(5x+1) is -(20)/((5x+1)^2)

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derivative of

f (x) = \frac{4}{5 x + 1}

- \frac{20}{( 5 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{5 x + 1})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{5 x + 1})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((5 x + 1)^{- 1})

Apply the chain rule:

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

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

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

= 4 (- \frac{1}{( 5 x + 1 ) ^{2}} \cdot 5)

Simplify

4 (- \frac{1}{( 5 x + 1 ) ^{2}} \cdot 5) : - \frac{20}{( 5 x + 1 ) ^{2}}

= - \frac{20}{( 5 x + 1 ) ^{2}}

\int \frac{2 x}{x ^{2} + 6} d x

5 y^{^{'}} = y^{2}

\frac{\partial}{\partial x} (ln (9 x^{2} + 5 y^{2}))

d er i v a t i v e ln (x y)

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = - 11

What is the derivative of f(x)= 4/(5x+1) ?
The derivative of f(x)= 4/(5x+1) is -(20)/((5x+1)^2)
What is the first derivative of f(x)= 4/(5x+1) ?
The first derivative of f(x)= 4/(5x+1) is -(20)/((5x+1)^2)