What is the derivative of $y=arcsin(x/7)$ ?

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Answer 1 · 2018-04-16T15:23:50

$d/dx arcsin(x/7)=(\sqrt{49-x^2})^{-1}$

We want to evaluate $d/dx arcsin(x/7)$ .

We can apply the chain rule, that $(f@g)'(x)=(f'@g)(x)g'(x)$ , and in our case $f=arcsin$ and $g(x)=1/7x$ . Therefore:

$d/dx arcsin(x/7)=\frac{1}{\sqrt{1-x^2/7^2}}\cdot d/dx x/7$

$d/dx arcsin(x/7)=\frac{1/7 d/dx x}{\sqrt{1-x^2/7^2}}$

$d/dx arcsin(x/7)=\frac{1}{7\sqrt{1-x^2/49}}$

We can further simplify this:

$d/dx arcsin(x/7)=\frac{1}{\sqrt{49(1-x^2/49)}}$

$d/dx arcsin(x/7)=(\sqrt{49-x^2})^{-1}$

What is the derivative of y=arcsin(x/7)y=arcsin(x/7)?