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

The derivative of-(81/((1+9x)^2)) is (1458)/((1+9x)^3)

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

The first derivative of-(81/((1+9x)^2)) is (1458)/((1+9x)^3)

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

\frac{1458}{( 1 + 9 x ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{2}{( 1 + 9 x ) ^{3}} \frac{d}{d x} (1 + 9 x)

= - \frac{2}{( 1 + 9 x ) ^{3}} \frac{d}{d x} (1 + 9 x)

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

= - 81 (- \frac{2}{( 1 + 9 x ) ^{3}} \cdot 9)

Simplify

- 81 (- \frac{2}{( 1 + 9 x ) ^{3}} \cdot 9) : \frac{1458}{( 1 + 9 x ) ^{3}}

= \frac{1458}{( 1 + 9 x ) ^{3}}

y = 5 x^{2}, y = 30 x - 45, [0, 45]

Y = Y = ln (x - 3)

\int sin (2 x) \cdot e^{x} d x

\int_{0}^{\frac{1}{5}} 2 arcsin (5 y) d y

f (x) = sin (x) csc (x)

What is the derivative of-(81/((1+9x)^2)) ?
The derivative of-(81/((1+9x)^2)) is (1458)/((1+9x)^3)
What is the first derivative of-(81/((1+9x)^2)) ?
The first derivative of-(81/((1+9x)^2)) is (1458)/((1+9x)^3)