What is the derivative of ln((2x+1^5)) ?

The derivative of ln((2x+1^5)) is (10)/(2x+1)

What is the first derivative of ln((2x+1^5)) ?

The first derivative of ln((2x+1^5)) is (10)/(2x+1)

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

\frac{10}{2 x + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((2 x + 1)^{5}) = 10 (2 x + 1)^{4}

= \frac{1}{( 2 x + 1 ) ^{5}} \cdot 10 (2 x + 1)^{4}

Simplify

\frac{1}{( 2 x + 1 ) ^{5}} \cdot 10 (2 x + 1)^{4} : \frac{10}{2 x + 1}

= \frac{10}{2 x + 1}

7 cos (x)

\int_{- \infty}^{0} x e^{- 8 x} d x

(1 + 2 x)^{2}

y = \frac{7 x}{e ^{x}}

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