What is the derivative of y=ln(x^4(x)) ?

The derivative of y=ln(x^4(x)) is 5/x

What is the first derivative of y=ln(x^4(x)) ?

The first derivative of y=ln(x^4(x)) is 5/x

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derivative of

y = ln (x^{4} (x))

\frac{5}{x}

Solution steps

\frac{d}{d x} (ln (x^{4} x))

Simplify

ln (x^{4} x) : ln (x^{5})

= \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}

f (x) = 3 x - x^{2}

\frac{d}{d x} (\frac{1}{ln ( ln ( ln ( x ) ) )})

f (x) = (2 x^{- 2} + 3)^{- 3}

tan (2 t)

\frac{d}{d x} (e^{x} (sin (x)))

What is the derivative of y=ln(x^4(x)) ?
The derivative of y=ln(x^4(x)) is 5/x
What is the first derivative of y=ln(x^4(x)) ?
The first derivative of y=ln(x^4(x)) is 5/x