What is the derivative of 1/((x+3^5)) ?

The derivative of 1/((x+3^5)) is -5/((x+3)^6)

What is the first derivative of 1/((x+3^5)) ?

The first derivative of 1/((x+3^5)) is -5/((x+3)^6)

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

- \frac{5}{( x + 3 ) ^{6}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{5}{( x + 3 ) ^{6}} \frac{d}{d x} (x + 3)

= - \frac{5}{( x + 3 ) ^{6}} \frac{d}{d x} (x + 3)

\frac{d}{d x} (x + 3) = 1

= - \frac{5}{( x + 3 ) ^{6}} \cdot 1

Simplify

= - \frac{5}{( x + 3 ) ^{6}}

What is the derivative of 1/((x+3^5)) ?
The derivative of 1/((x+3^5)) is -5/((x+3)^6)
What is the first derivative of 1/((x+3^5)) ?
The first derivative of 1/((x+3^5)) is -5/((x+3)^6)