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

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

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

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

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\frac{d}{d x} (x^{a r c s i n (x)})

x^{a r c s i n (x)} (\frac{ln ( x )}{1 - x ^{2}} + \frac{arcsin ( x )}{x})

Solution steps

\frac{d}{d x} (x^{a r c s i n (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{a r c s i n (x)} = e^{a r c s i n (x) l n (x)}

= \frac{d}{d x} (e^{a r c s i n (x) l n (x)})

Apply the chain rule:

e^{a r c s i n (x) l n (x)} \frac{d}{d x} (arcsin (x) ln (x))

= e^{a r c s i n (x) l n (x)} \frac{d}{d x} (arcsin (x) ln (x))

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

= e^{a r c s i n (x) l n (x)} (\frac{ln ( x )}{1 - x ^{2}} + \frac{arcsin ( x )}{x})

e^{a r c s i n (x) l n (x)} = x^{a r c s i n (x)}

= x^{a r c s i n (x)} (\frac{ln ( x )}{1 - x ^{2}} + \frac{arcsin ( x )}{x})

\frac{d}{d x} (\frac{4 x + 4 1 + x}{x ^{2} - 1})

\int \frac{8 x ^{2} + 10}{x ^{3} + 5 x} d x

x^{3} = \frac{2 y ^{5} + 4}{5 y ^{4} y ^{^{'}}}

\int sin (16 x) cos (7 x) d x

\frac{\partial}{\partial x} (x^{7} y^{6})

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