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Popular >

derivative of ln(x(1-x)^8)

Solution

derivative of

ln (x (1 - x)^{8})

Solution

\frac{1 - 9 x}{x ( - x + 1 )}

Solution steps

\frac{d}{d x} (ln (x (1 - x)^{8}))

Apply the chain rule:

\frac{1}{x ( 1 - x ) ^{8}} \frac{d}{d x} (x (1 - x)^{8})

= \frac{1}{x ( 1 - x ) ^{8}} \frac{d}{d x} (x (1 - x)^{8})

\frac{d}{d x} (x (1 - x)^{8}) = (1 - x)^{8} - 8 x (1 - x)^{7}

= \frac{1}{x ( 1 - x ) ^{8}} ((1 - x)^{8} - 8 x (1 - x)^{7})

Simplify

\frac{1}{x ( 1 - x ) ^{8}} ((1 - x)^{8} - 8 x (1 - x)^{7}) : \frac{1 - 9 x}{x ( - x + 1 )}

= \frac{1 - 9 x}{x ( - x + 1 )}

Graph

Popular Examples

(d^2)/(dx^2)(e^{7x^2})

\frac{d ^{2}}{d x ^{2}} (e^{7 x^{2}})

(d^2)/(d{r)(T)dT}({r}(T)(T)^2(d^2)/(d{r)(T)dT}(T))

\frac{d ^{2}}{d r ( T ) d T} (r (T) (T)^{2} \frac{d ^{2}}{d r ( T ) d T} (T))

derivative of cos(3)

\frac{d}{d x} (cos (3))

f (t) = - 4 sin (t)

(\partial)/(\partial x)(e^{-9x})

\frac{\partial}{\partial x} (e^{- 9 x})

Frequently Asked Questions (FAQ)

What is the derivative of ln(x(1-x)^8) ?
The derivative of ln(x(1-x)^8) is (1-9x)/(x(-x+1))
What is the first derivative of ln(x(1-x)^8) ?
The first derivative of ln(x(1-x)^8) is (1-9x)/(x(-x+1))