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

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

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

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

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derivative of

f (x) = 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{d}{d x} (2 + 5 x)

\int_{4}^{5} x x^{2} - 16 d x

\frac{\partial}{\partial x} (\frac{1}{3} (x^{2} + 2)^{\frac{3}{2}})

x \to \infty lim (9 x^{2} + x - 3)

\int \frac{1}{y ^{3} + y} d y

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