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Popular >

derivative of 1/9 x-ln(3x)

Solution

\frac{d}{d x} (\frac{1}{9} x - ln (3 x))

Solution

\frac{1}{9} - \frac{1}{x}

Solution steps

\frac{d}{d x} (\frac{1}{9} x - ln (3 x))

Simplify

\frac{1}{9} x - ln (3 x) : \frac{x}{9} - ln (3 x)

= \frac{d}{d x} (\frac{x}{9} - ln (3 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x}{9}) - \frac{d}{d x} (ln (3 x))

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= \frac{1}{9} - \frac{1}{x}

Popular Examples

derivative of 6sqrt(x)+3\sqrt[3]{x}derivative of

area y=x^2,y=sqrt(8x)area

y = x^{2}, y = 8 x

y^'-6x^2y=0,y(1)=e

y^{^{'}} - 6 x^{2} y = 0, y (1) = e

derivative of y=((x+4)(x^2-4x+16))/(x^3)derivative of

y = \frac{( x + 4 ) ( x ^{2} - 4 x + 16 )}{x ^{3}}

limit as x approaches 2 of 2/(4x+3)

x \to 2 lim (\frac{2}{4 x + 3})

Frequently Asked Questions (FAQ)

What is the derivative of 1/9 x-ln(3x) ?
The derivative of 1/9 x-ln(3x) is 1/9-1/x
What is the first derivative of 1/9 x-ln(3x) ?
The first derivative of 1/9 x-ln(3x) is 1/9-1/x