What is the derivative of f(x)= 1/((3x+8)^2) ?

The derivative of f(x)= 1/((3x+8)^2) is -6/((3x+8)^3)

What is the first derivative of f(x)= 1/((3x+8)^2) ?

The first derivative of f(x)= 1/((3x+8)^2) is -6/((3x+8)^3)

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derivative of

f (x) = \frac{1}{( 3 x + 8 ) ^{2}}

- \frac{6}{( 3 x + 8 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{1}{( 3 x + 8 ) ^{2}})

Apply exponent rule:

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

= \frac{d}{d x} ((3 x + 8)^{- 2})

Apply the chain rule:

- \frac{2}{( 3 x + 8 ) ^{3}} \frac{d}{d x} (3 x + 8)

= - \frac{2}{( 3 x + 8 ) ^{3}} \frac{d}{d x} (3 x + 8)

\frac{d}{d x} (3 x + 8) = 3

= - \frac{2}{( 3 x + 8 ) ^{3}} \cdot 3

Simplify

- \frac{2}{( 3 x + 8 ) ^{3}} \cdot 3 : - \frac{6}{( 3 x + 8 ) ^{3}}

= - \frac{6}{( 3 x + 8 ) ^{3}}

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

\int cos (2 πn x) d x

n = 0 \sum \infty \frac{( x - 3 ) ^{n}}{n}

\frac{d}{d x} (\frac{1}{e ^{\frac{1}{x}}})

\frac{d}{d x} (2 x - 9)

What is the derivative of f(x)= 1/((3x+8)^2) ?
The derivative of f(x)= 1/((3x+8)^2) is -6/((3x+8)^3)
What is the first derivative of f(x)= 1/((3x+8)^2) ?
The first derivative of f(x)= 1/((3x+8)^2) is -6/((3x+8)^3)