What is the derivative of-(10/((1+5x)^2)) ?

The derivative of-(10/((1+5x)^2)) is (100)/((1+5x)^3)

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

The first derivative of-(10/((1+5x)^2)) is (100)/((1+5x)^3)

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\frac{d}{d x} (- \frac{10}{( 1 + 5 x ) ^{2}})

\frac{100}{( 1 + 5 x ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{10}{( 1 + 5 x ) ^{2}})

Take the constant out:

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

= - 10 \frac{d}{d x} (\frac{1}{( 1 + 5 x ) ^{2}})

Apply exponent rule:

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

= - 10 \frac{d}{d x} ((1 + 5 x)^{- 2})

Apply the chain rule:

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

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

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

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

Simplify

- 10 (- \frac{2}{( 1 + 5 x ) ^{3}} \cdot 5) : \frac{100}{( 1 + 5 x ) ^{3}}

= \frac{100}{( 1 + 5 x ) ^{3}}

\frac{\partial}{\partial x} (\frac{x + 4}{y + 6})

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

x y^{^{'}} + y = 3 cos (x)

\frac{\partial}{\partial x} (\frac{6}{5} - \frac{6}{5} e^{- 20 x})

n = 2 \sum \infty \frac{3}{n \cdot ( n + 3 )}

What is the derivative of-(10/((1+5x)^2)) ?
The derivative of-(10/((1+5x)^2)) is (100)/((1+5x)^3)
What is the first derivative of-(10/((1+5x)^2)) ?
The first derivative of-(10/((1+5x)^2)) is (100)/((1+5x)^3)