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

The derivative of ln(x^5) is 5/x

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

The first derivative of ln(x^5) is 5/x

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derivative of

ln (x^{5})

\frac{5}{x}

Solution steps

\frac{d}{d x} (ln (x^{5}))

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{1}{x ^{5}} \cdot 5 x^{4}

Simplify

\frac{1}{x ^{5}} \cdot 5 x^{4} : \frac{5}{x}

= \frac{5}{x}

(\frac{4}{5} x)^{4}

\frac{\partial}{\partial x} (x - w)

x y^{^{'}} + 4 y = \frac{2 e ^{- 4 x}}{x ^{3}}

y = - 3 x^{2} + 10 x + 2, at x = 1

\frac{t d u}{d t} = t^{2} + 3 u, t > 0, H (6) = 180

What is the derivative of ln(x^5) ?
The derivative of ln(x^5) is 5/x
What is the first derivative of ln(x^5) ?
The first derivative of ln(x^5) is 5/x