What is the derivative of (64)/((1+4x)^3) ?

The derivative of (64)/((1+4x)^3) is -(768)/((1+4x)^4)

What is the first derivative of (64)/((1+4x)^3) ?

The first derivative of (64)/((1+4x)^3) is -(768)/((1+4x)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{64}{( 1 + 4 x ) ^{3}}

- \frac{768}{( 1 + 4 x ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{64}{( 1 + 4 x ) ^{3}})

Take the constant out:

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

= 64 \frac{d}{d x} (\frac{1}{( 1 + 4 x ) ^{3}})

Apply exponent rule:

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

= 64 \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

= 64 (- \frac{3}{( 1 + 4 x ) ^{4}} \cdot 4)

Simplify

64 (- \frac{3}{( 1 + 4 x ) ^{4}} \cdot 4) : - \frac{768}{( 1 + 4 x ) ^{4}}

= - \frac{768}{( 1 + 4 x ) ^{4}}

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

x \to 9 lim (8 x + ∣ x - 9 ∣)

\frac{\partial}{\partial y} (2 x y^{3} - 3)

4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 3 x

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

What is the derivative of (64)/((1+4x)^3) ?
The derivative of (64)/((1+4x)^3) is -(768)/((1+4x)^4)
What is the first derivative of (64)/((1+4x)^3) ?
The first derivative of (64)/((1+4x)^3) is -(768)/((1+4x)^4)