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Popular >

derivative of ln(x^{9/2})

Solution

\frac{d}{d x} (ln (x^{\frac{9}{2}}))

Solution

\frac{9}{2 x}

Solution steps

\frac{d}{d x} (ln (x^{\frac{9}{2}}))

Apply the chain rule:

\frac{1}{x ^{\frac{9}{2}}} \frac{d}{d x} (x^{\frac{9}{2}})

= \frac{1}{x ^{\frac{9}{2}}} \frac{d}{d x} (x^{\frac{9}{2}})

\frac{d}{d x} (x^{\frac{9}{2}}) = \frac{9 x ^{\frac{7}{2}}}{2}

= \frac{1}{x ^{\frac{9}{2}}} \cdot \frac{9 x ^{\frac{7}{2}}}{2}

Simplify

\frac{1}{x ^{\frac{9}{2}}} \cdot \frac{9 x ^{\frac{7}{2}}}{2} : \frac{9}{2 x}

= \frac{9}{2 x}

Popular Examples

integral of (16)/((x^2-4)(x-2))

\int \frac{16}{( x ^{2} - 4 ) ( x - 2 )} d x

((((dy)/(dx))-e^{-x}+5))/y =-5

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

derivative of x^{0.3}

\frac{d}{d x} (x^{0.3})

integral of 2cos^2(3x)

\int 2 cos^{2} (3 x) d x

limit as x approaches infinity of 9/2

x \to \infty lim (\frac{9}{2})

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^{9/2}) ?
The derivative of ln(x^{9/2}) is 9/(2x)
What is the first derivative of ln(x^{9/2}) ?
The first derivative of ln(x^{9/2}) is 9/(2x)