What is the derivative of y=arcsin(3sqrt(5x)) ?

The derivative of y=arcsin(3sqrt(5x)) is (3sqrt(5))/(2sqrt(x)\sqrt{1-45x)}

What is the first derivative of y=arcsin(3sqrt(5x)) ?

The first derivative of y=arcsin(3sqrt(5x)) is (3sqrt(5))/(2sqrt(x)\sqrt{1-45x)}

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derivative of

y = arcsin (3 5 x)

\frac{3 5}{2 x 1 - 45 x}

Solution steps

\frac{d}{d x} (arcsin (3 5 x))

Simplify

arcsin (3 5 x) : arcsin (35 x)

= \frac{d}{d x} (arcsin (35 x))

Apply the chain rule:

\frac{1}{1 - ( 3 5 x ) ^{2}} \frac{d}{d x} (35 x)

= \frac{1}{1 - ( 3 5 x ) ^{2}} \frac{d}{d x} (35 x)

\frac{d}{d x} (35 x) = \frac{3 5}{2 x}

= \frac{1}{1 - ( 3 5 x ) ^{2}} \cdot \frac{3 5}{2 x}

Simplify

\frac{1}{1 - ( 3 5 x ) ^{2}} \cdot \frac{3 5}{2 x} : \frac{3 5}{2 x 1 - 45 x}

= \frac{3 5}{2 x 1 - 45 x}

What is the derivative of y=arcsin(3sqrt(5x)) ?
The derivative of y=arcsin(3sqrt(5x)) is (3sqrt(5))/(2sqrt(x)\sqrt{1-45x)}
What is the first derivative of y=arcsin(3sqrt(5x)) ?
The first derivative of y=arcsin(3sqrt(5x)) is (3sqrt(5))/(2sqrt(x)\sqrt{1-45x)}