What is the derivative of (1-x)^3-log_{e}(1-x) ?

The derivative of (1-x)^3-log_{e}(1-x) is (1+6x-9x^2+3x^3)/(1-x)-3

What is the first derivative of (1-x)^3-log_{e}(1-x) ?

The first derivative of (1-x)^3-log_{e}(1-x) is (1+6x-9x^2+3x^3)/(1-x)-3

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derivative of

(1 - x)^{3} - lo g_{e} (1 - x)

\frac{1 + 6 x - 9 x ^{2} + 3 x ^{3}}{1 - x} - 3

Solution steps

\frac{d}{d x} ((1 - x)^{3} - lo g_{e} (1 - x))

Simplify

(1 - x)^{3} - lo g_{e} (1 - x) : (1 - x)^{3} - ln (1 - x)

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} ((1 - x)^{3}) = - 3 (1 - x)^{2}

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

= - 3 (1 - x)^{2} - (- \frac{1}{1 - x})

Simplify

- 3 (1 - x)^{2} - (- \frac{1}{1 - x}) : \frac{1 + 6 x - 9 x ^{2} + 3 x ^{3}}{1 - x} - 3

= \frac{1 + 6 x - 9 x ^{2} + 3 x ^{3}}{1 - x} - 3

\frac{5 x ^{2}}{3 x - 1}

\int_{1}^{2} 3 - \frac{6}{x ^{2}} d x

\int \frac{6 cosh ( x )}{x} d x

y^{^{'''}} + 4 y^{^{''}} - 16 y^{^{'}} - 64 y = 0

\frac{d}{d x} (5 cos (x) - cos (5 x))

What is the derivative of (1-x)^3-log_{e}(1-x) ?
The derivative of (1-x)^3-log_{e}(1-x) is (1+6x-9x^2+3x^3)/(1-x)-3
What is the first derivative of (1-x)^3-log_{e}(1-x) ?
The first derivative of (1-x)^3-log_{e}(1-x) is (1+6x-9x^2+3x^3)/(1-x)-3