What is the derivative of 1/(1+5x) ?

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

What is the first derivative of 1/(1+5x) ?

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (a sin^{3} (x))

x \to 0 - lim (\frac{14 x ^{3} + 15 x}{x})

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

y^{^{''}} - 4 y + 4 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

x \to + 0 lim (3^{x} + 7)

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