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Popular >

derivative of (1/(3x+1)^4)

Solution

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

Solution

- \frac{12}{( 3 x + 1 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

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

= 4 (\frac{1}{3 x + 1})^{3} (- \frac{3}{( 3 x + 1 ) ^{2}})

Simplify

4 (\frac{1}{3 x + 1})^{3} (- \frac{3}{( 3 x + 1 ) ^{2}}) : - \frac{12}{( 3 x + 1 ) ^{5}}

= - \frac{12}{( 3 x + 1 ) ^{5}}

Popular Examples

inverse oflaplace 4/(s^2+9)inverse laplace

\frac{4}{s ^{2} + 9}

(dy)/(dx)=1-2y,y(0)=0

\frac{d y}{d x} = 1 - 2 y, y (0) = 0

integral of 11sin^5(x)

\int 11 sin^{5} (x) d x

(dy)/(dx)=(((2y+7))/((4x+9)))^2

\frac{d y}{d x} = (\frac{( 2 y + 7 )}{( 4 x + 9 )})^{2}

integral of (x^2)/(2-x^3)

\int \frac{x ^{2}}{2 - x ^{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (1/(3x+1)^4) ?
The derivative of (1/(3x+1)^4) is -(12)/((3x+1)^5)
What is the first derivative of (1/(3x+1)^4) ?
The first derivative of (1/(3x+1)^4) is -(12)/((3x+1)^5)