What is the derivative of 3-ln(6x-(x^2)/(12)+x) ?

The derivative of 3-ln(6x-(x^2)/(12)+x) is -x/6-1/x+1

What is the first derivative of 3-ln(6x-(x^2)/(12)+x) ?

The first derivative of 3-ln(6x-(x^2)/(12)+x) is -x/6-1/x+1

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\frac{d}{d x} (3 - ln (6 x) - \frac{x ^{2}}{12} + x)

- \frac{x}{6} - \frac{1}{x} + 1

Solution steps

\frac{d}{d x} (3 - ln (6 x) - \frac{x ^{2}}{12} + x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3) - \frac{d}{d x} (ln (6 x)) - \frac{d}{d x} (\frac{x ^{2}}{12}) + \frac{d x}{d x}

\frac{d}{d x} (3) = 0

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

\frac{d}{d x} (\frac{x ^{2}}{12}) = \frac{x}{6}

\frac{d x}{d x} = 1

= 0 - \frac{1}{x} - \frac{x}{6} + 1

Simplify

= - \frac{x}{6} - \frac{1}{x} + 1

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

3 t^{2} + 25

x \to - 4 - lim (\frac{1}{x ^{2} - 16})

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

\frac{d}{d x} (e^{- \frac{x}{t}})

What is the derivative of 3-ln(6x-(x^2)/(12)+x) ?
The derivative of 3-ln(6x-(x^2)/(12)+x) is -x/6-1/x+1
What is the first derivative of 3-ln(6x-(x^2)/(12)+x) ?
The first derivative of 3-ln(6x-(x^2)/(12)+x) is -x/6-1/x+1