What is the derivative of sqrt(log_{a)(-x^2-x}) ?

The derivative of sqrt(log_{a)(-x^2-x}) is (-2x-1)/(2ln(a)sqrt(log_{a)(-x^2-x))(-x^2-x)}

What is the first derivative of sqrt(log_{a)(-x^2-x}) ?

The first derivative of sqrt(log_{a)(-x^2-x}) is (-2x-1)/(2ln(a)sqrt(log_{a)(-x^2-x))(-x^2-x)}

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\frac{d}{d x} (lo g_{a} (- x^{2} - x))

\frac{- 2 x - 1}{2 ln ( a ) lo g _{a} ( - x ^{2} - x ) ( - x ^{2} - x )}

Solution steps

\frac{d}{d x} (lo g_{a} (- x^{2} - x))

Apply the chain rule:

\frac{1}{2 lo g _{a} ( - x ^{2} - x )} \frac{d}{d x} (lo g_{a} (- x^{2} - x))

= \frac{1}{2 lo g _{a} ( - x ^{2} - x )} \frac{d}{d x} (lo g_{a} (- x^{2} - x))

\frac{d}{d x} (lo g_{a} (- x^{2} - x)) = \frac{- 2 x - 1}{ln ( a ) ( - x ^{2} - x )}

= \frac{1}{2 lo g _{a} ( - x ^{2} - x )} \cdot \frac{- 2 x - 1}{ln ( a ) ( - x ^{2} - x )}

Simplify

\frac{1}{2 lo g _{a} ( - x ^{2} - x )} \cdot \frac{- 2 x - 1}{ln ( a ) ( - x ^{2} - x )} : \frac{- 2 x - 1}{2 ln ( a ) lo g _{a} ( - x ^{2} - x ) ( - x ^{2} - x )}

= \frac{- 2 x - 1}{2 ln ( a ) lo g _{a} ( - x ^{2} - x ) ( - x ^{2} - x )}

\frac{d}{d x} ((e^{3 x} - 1)^{5})

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

f (x) = 2 x^{2} + 8 x - 2

\frac{7}{x ^{2}}

x \to \infty lim (\frac{4 ^{x}}{5 ^{x + 1}})

What is the derivative of sqrt(log_{a)(-x^2-x}) ?
The derivative of sqrt(log_{a)(-x^2-x}) is (-2x-1)/(2ln(a)sqrt(log_{a)(-x^2-x))(-x^2-x)}
What is the first derivative of sqrt(log_{a)(-x^2-x}) ?
The first derivative of sqrt(log_{a)(-x^2-x}) is (-2x-1)/(2ln(a)sqrt(log_{a)(-x^2-x))(-x^2-x)}