What is the derivative of f(x)=-1/((5x+1)^2) ?

The derivative of f(x)=-1/((5x+1)^2) is (10)/((5x+1)^3)

What is the first derivative of f(x)=-1/((5x+1)^2) ?

The first derivative of f(x)=-1/((5x+1)^2) is (10)/((5x+1)^3)

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derivative of

f (x) = - \frac{1}{( 5 x + 1 ) ^{2}}

\frac{10}{( 5 x + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{1}{( 5 x + 1 ) ^{2}})

Take the constant out:

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

= - \frac{d}{d x} (\frac{1}{( 5 x + 1 ) ^{2}})

Apply exponent rule:

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

= - \frac{d}{d x} ((5 x + 1)^{- 2})

Apply the chain rule:

- \frac{2}{( 5 x + 1 ) ^{3}} \frac{d}{d x} (5 x + 1)

= - \frac{2}{( 5 x + 1 ) ^{3}} \frac{d}{d x} (5 x + 1)

\frac{d}{d x} (5 x + 1) = 5

= - (- \frac{2}{( 5 x + 1 ) ^{3}} \cdot 5)

Simplify

- (- \frac{2}{( 5 x + 1 ) ^{3}} \cdot 5) : \frac{10}{( 5 x + 1 ) ^{3}}

= \frac{10}{( 5 x + 1 ) ^{3}}

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What is the derivative of f(x)=-1/((5x+1)^2) ?
The derivative of f(x)=-1/((5x+1)^2) is (10)/((5x+1)^3)
What is the first derivative of f(x)=-1/((5x+1)^2) ?
The first derivative of f(x)=-1/((5x+1)^2) is (10)/((5x+1)^3)