What is the derivative of f(x)=arcsin(x^6) ?

The derivative of f(x)=arcsin(x^6) is (6x^5)/(sqrt(1-x^{12))}

What is the first derivative of f(x)=arcsin(x^6) ?

The first derivative of f(x)=arcsin(x^6) is (6x^5)/(sqrt(1-x^{12))}

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derivative of

f (x) = arcsin (x^{6})

\frac{6 x ^{5}}{1 - x ^{12}}

Solution steps

\frac{d}{d x} (arcsin (x^{6}))

Apply the chain rule:

\frac{1}{1 - ( x ^{6} ) ^{2}} \frac{d}{d x} (x^{6})

= \frac{1}{1 - ( x ^{6} ) ^{2}} \frac{d}{d x} (x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{1}{1 - ( x ^{6} ) ^{2}} \cdot 6 x^{5}

Simplify

\frac{1}{1 - ( x ^{6} ) ^{2}} \cdot 6 x^{5} : \frac{6 x ^{5}}{1 - x ^{12}}

= \frac{6 x ^{5}}{1 - x ^{12}}

What is the derivative of f(x)=arcsin(x^6) ?
The derivative of f(x)=arcsin(x^6) is (6x^5)/(sqrt(1-x^{12))}
What is the first derivative of f(x)=arcsin(x^6) ?
The first derivative of f(x)=arcsin(x^6) is (6x^5)/(sqrt(1-x^{12))}