What is the derivative of arccos(x^{1/2}) ?

The derivative of arccos(x^{1/2}) is -1/(2x^{1/2)sqrt(1-x)}

What is the first derivative of arccos(x^{1/2}) ?

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

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derivative of

arccos (x^{\frac{1}{2}})

- \frac{1}{2 x ^{\frac{1}{2}} 1 - x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{2 x ^{\frac{1}{2}} 1 - x}

4 x^{3} + e^{16 x} - 3^{2 x - 1}

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

- x^{4} + 2 x^{3} - 5 x^{2} + 0.4

\int_{1}^{4} 3 x d x

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