What is the derivative of (54/((3x+1)^4)) ?

The derivative of (54/((3x+1)^4)) is -(648)/((3x+1)^5)

What is the first derivative of (54/((3x+1)^4)) ?

The first derivative of (54/((3x+1)^4)) is -(648)/((3x+1)^5)

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\frac{d}{d x} (\frac{54}{( 3 x + 1 ) ^{4}})

- \frac{648}{( 3 x + 1 ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{54}{( 3 x + 1 ) ^{4}})

Take the constant out:

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

= 54 \frac{d}{d x} (\frac{1}{( 3 x + 1 ) ^{4}})

Apply exponent rule:

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

= 54 \frac{d}{d x} ((3 x + 1)^{- 4})

Apply the chain rule:

- \frac{4}{( 3 x + 1 ) ^{5}} \frac{d}{d x} (3 x + 1)

= - \frac{4}{( 3 x + 1 ) ^{5}} \frac{d}{d x} (3 x + 1)

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

= 54 (- \frac{4}{( 3 x + 1 ) ^{5}} \cdot 3)

Simplify

54 (- \frac{4}{( 3 x + 1 ) ^{5}} \cdot 3) : - \frac{648}{( 3 x + 1 ) ^{5}}

= - \frac{648}{( 3 x + 1 ) ^{5}}

x^{2} y^{^{'}} + 2 x y = 9 cos^{2} (x)

\frac{\partial}{\partial t} (x^{2} sin (3 t))

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

x \to 1 + lim (∣ x ∣)

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

What is the derivative of (54/((3x+1)^4)) ?
The derivative of (54/((3x+1)^4)) is -(648)/((3x+1)^5)
What is the first derivative of (54/((3x+1)^4)) ?
The first derivative of (54/((3x+1)^4)) is -(648)/((3x+1)^5)