What is the derivative of (128/((1+4x)^3)) ?

The derivative of (128/((1+4x)^3)) is -(1536)/((1+4x)^4)

What is the first derivative of (128/((1+4x)^3)) ?

The first derivative of (128/((1+4x)^3)) is -(1536)/((1+4x)^4)

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\frac{d}{d x} (\frac{128}{( 1 + 4 x ) ^{3}})

- \frac{1536}{( 1 + 4 x ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{128}{( 1 + 4 x ) ^{3}})

Take the constant out:

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

= 128 \frac{d}{d x} (\frac{1}{( 1 + 4 x ) ^{3}})

Apply exponent rule:

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

= 128 \frac{d}{d x} ((1 + 4 x)^{- 3})

Apply the chain rule:

- \frac{3}{( 1 + 4 x ) ^{4}} \frac{d}{d x} (1 + 4 x)

= - \frac{3}{( 1 + 4 x ) ^{4}} \frac{d}{d x} (1 + 4 x)

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

= 128 (- \frac{3}{( 1 + 4 x ) ^{4}} \cdot 4)

Simplify

128 (- \frac{3}{( 1 + 4 x ) ^{4}} \cdot 4) : - \frac{1536}{( 1 + 4 x ) ^{4}}

= - \frac{1536}{( 1 + 4 x ) ^{4}}

\frac{d ^{2}}{d x ^{2}} (∣ x ∣)

\frac{d}{d t} (t e^{- 3 t})

\frac{d}{d x} (\frac{6 ( x ^{2} + 1 )}{( x ^{2} - 3 ) ^{3}})

e^{x}, x e^{x^{2}}, 0, 1

What is the derivative of (128/((1+4x)^3)) ?
The derivative of (128/((1+4x)^3)) is -(1536)/((1+4x)^4)
What is the first derivative of (128/((1+4x)^3)) ?
The first derivative of (128/((1+4x)^3)) is -(1536)/((1+4x)^4)