What is the derivative of f(x)=arcsin(5x) ?

The derivative of f(x)=arcsin(5x) is 5/(sqrt(1-25x^2))

What is the first derivative of f(x)=arcsin(5x) ?

The first derivative of f(x)=arcsin(5x) is 5/(sqrt(1-25x^2))

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derivative of

f (x) = arcsin (5 x)

\frac{5}{1 - 25 x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{1 - ( 5 x ) ^{2}} \cdot 5 : \frac{5}{1 - 25 x ^{2}}

= \frac{5}{1 - 25 x ^{2}}

x \to 1 lim (\frac{- 1}{x - 1})

2 y^{^{''}} + y^{^{'}} - 3 y = 0, y (0) = a, y^{^{'}} (0) = b

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What is the derivative of f(x)=arcsin(5x) ?
The derivative of f(x)=arcsin(5x) is 5/(sqrt(1-25x^2))
What is the first derivative of f(x)=arcsin(5x) ?
The first derivative of f(x)=arcsin(5x) is 5/(sqrt(1-25x^2))