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

The derivative of 4/(1+4x) is -(16)/((1+4x)^2)

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

The first derivative of 4/(1+4x) is -(16)/((1+4x)^2)

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

- \frac{16}{( 1 + 4 x ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

4 (- \frac{1}{( 1 + 4 x ) ^{2}} \cdot 4) : - \frac{16}{( 1 + 4 x ) ^{2}}

= - \frac{16}{( 1 + 4 x ) ^{2}}

\int x \cdot sec^{2} (x) d x

\frac{\partial}{\partial x} (\frac{x + 4}{y + 1})

\frac{d}{d x} (\frac{2 x}{3 y ^{2}})

\int cos^{3} (1) d x

f (x) = (3 x + 2) (4 x^{2} + 3)

What is the derivative of 4/(1+4x) ?
The derivative of 4/(1+4x) is -(16)/((1+4x)^2)
What is the first derivative of 4/(1+4x) ?
The first derivative of 4/(1+4x) is -(16)/((1+4x)^2)