What is the derivative of log_{10}((arcsin(x)^2)) ?

The derivative of log_{10}((arcsin(x)^2)) is 2/(ln(10)arcsin(x)sqrt(-x^2+1))

What is the first derivative of log_{10}((arcsin(x)^2)) ?

The first derivative of log_{10}((arcsin(x)^2)) is 2/(ln(10)arcsin(x)sqrt(-x^2+1))

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\frac{d}{d x} (lo g_{10} ((arcsin (x))^{2}))

\frac{2}{ln ( 10 ) arcsin ( x ) - x ^{2} + 1}

Solution steps

\frac{d}{d x} (lo g_{10} ((arcsin (x))^{2}))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} \frac{ln ( ( arcsin ( x ) ) ^{2} )}{ln ( 10 )}

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln ((arcsin (x))^{2}))

Apply the chain rule:

\frac{1}{( arcsin ( x ) ) ^{2}} \frac{d}{d x} ((arcsin (x))^{2})

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

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

= \frac{1}{ln ( 10 )} \cdot \frac{1}{( arcsin ( x ) ) ^{2}} \cdot \frac{2 arcsin ( x )}{1 - x ^{2}}

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{arcsin ^{2} ( x )} \cdot \frac{2 arcsin ( x )}{1 - x ^{2}} : \frac{2}{ln ( 10 ) arcsin ( x ) - x ^{2} + 1}

= \frac{2}{ln ( 10 ) arcsin ( x ) - x ^{2} + 1}

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

\frac{\partial}{\partial x} (y^{4} - 6 x y)

y^{^{'}} + 4 y = e^{3 x}

x \to 0 lim (\frac{1}{1})

\int (x^{2} + 6) sin (2 x) d x

What is the derivative of log_{10}((arcsin(x)^2)) ?
The derivative of log_{10}((arcsin(x)^2)) is 2/(ln(10)arcsin(x)sqrt(-x^2+1))
What is the first derivative of log_{10}((arcsin(x)^2)) ?
The first derivative of log_{10}((arcsin(x)^2)) is 2/(ln(10)arcsin(x)sqrt(-x^2+1))