What is (\partial)/(\partial x)(arcsin(5x)) ?

The answer to (\partial)/(\partial x)(arcsin(5x)) is 5/(sqrt(1-25x^2))

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(\partial)/(\partial x)(arcsin(5x))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}}

y^{^{''''}} + 4 y^{^{''}} = 0

x \to 1 lim (x ln (x) - x)

\frac{\partial}{\partial x} ((x + y) e^{y})

\int \frac{k}{r} (- \frac{r ^{2}}{4}) d r

\int \frac{1}{x ^{2} 400 - x ^{2}} d x

What is (\partial)/(\partial x)(arcsin(5x)) ?
The answer to (\partial)/(\partial x)(arcsin(5x)) is 5/(sqrt(1-25x^2))