What is the derivative of x-1-ln(x) ?

The derivative of x-1-ln(x) is -1/x+1

What is the first derivative of x-1-ln(x) ?

The first derivative of x-1-ln(x) is -1/x+1

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

- \frac{1}{x} + 1

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (1) = 0

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

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

Simplify

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

x^{2} (1 - y) \frac{d y}{d x} + y^{2} (1 + x) = 0

\frac{d y}{d t} - 2 y = 8 e^{4 t}

\int \frac{1}{27} e^{3 x} d x

x \to 0 + lim (\frac{9 x}{sin ( x )})

4 x^{3} e^{x} + e^{x} x^{4}

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