What is the derivative of 9/(1+9x) ?

The derivative of 9/(1+9x) is -(81)/((1+9x)^2)

What is the first derivative of 9/(1+9x) ?

The first derivative of 9/(1+9x) is -(81)/((1+9x)^2)

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\frac{d}{d x} (\frac{9}{1 + 9 x})

- \frac{81}{( 1 + 9 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{9}{1 + 9 x})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{1 + 9 x})

Apply exponent rule:

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

= 9 \frac{d}{d x} ((1 + 9 x)^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 9 x ) ^{2}} \frac{d}{d x} (1 + 9 x)

= - \frac{1}{( 1 + 9 x ) ^{2}} \frac{d}{d x} (1 + 9 x)

\frac{d}{d x} (1 + 9 x) = 9

= 9 (- \frac{1}{( 1 + 9 x ) ^{2}} \cdot 9)

Simplify

9 (- \frac{1}{( 1 + 9 x ) ^{2}} \cdot 9) : - \frac{81}{( 1 + 9 x ) ^{2}}

= - \frac{81}{( 1 + 9 x ) ^{2}}

f (x) = t^{5} sin (t)

\int_{0}^{1} 1 + 144 x d x

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

t^{2} t

x \to 0 + lim (x ln (x))

What is the derivative of 9/(1+9x) ?
The derivative of 9/(1+9x) is -(81)/((1+9x)^2)
What is the first derivative of 9/(1+9x) ?
The first derivative of 9/(1+9x) is -(81)/((1+9x)^2)