What is the derivative of ln(3^{sqrt(2-x^2)}) ?

The derivative of ln(3^{sqrt(2-x^2)}) is -(ln(3)x)/(sqrt(2-x^2))

What is the first derivative of ln(3^{sqrt(2-x^2)}) ?

The first derivative of ln(3^{sqrt(2-x^2)}) is -(ln(3)x)/(sqrt(2-x^2))

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

- \frac{ln ( 3 ) x}{2 - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{3 ^{2 - x^{2}}} (- \frac{ln ( 3 ) \cdot 3 ^{2 - x^{2}} x}{2 - x ^{2}}) : - \frac{ln ( 3 ) x}{2 - x ^{2}}

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

\int_{- 1}^{0} \frac{1}{1 + x} d x

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

y = 4 x^{3}, (- 1, - 4)

x \to \frac{1}{2} lim (\frac{x + 1}{x + 5})

\frac{d y}{d x} = - \frac{3 y}{x} - 2 - x^{- 4}

What is the derivative of ln(3^{sqrt(2-x^2)}) ?
The derivative of ln(3^{sqrt(2-x^2)}) is -(ln(3)x)/(sqrt(2-x^2))
What is the first derivative of ln(3^{sqrt(2-x^2)}) ?
The first derivative of ln(3^{sqrt(2-x^2)}) is -(ln(3)x)/(sqrt(2-x^2))