What is (\partial)/(\partial x)(arcsin(4x)) ?

The answer to (\partial)/(\partial x)(arcsin(4x)) is 4/(sqrt(1-16x^2))

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(\partial)/(\partial x)(arcsin(4x))

\frac{\partial}{\partial x} (arcsin (4 x))

\frac{4}{1 - 16 x ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (4 x))

Apply the chain rule:

\frac{1}{1 - ( 4 x ) ^{2}} \frac{\partial}{\partial x} (4 x)

= \frac{1}{1 - ( 4 x ) ^{2}} \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= \frac{1}{1 - ( 4 x ) ^{2}} \cdot 4

Simplify

\frac{1}{1 - ( 4 x ) ^{2}} \cdot 4 : \frac{4}{1 - 16 x ^{2}}

= \frac{4}{1 - 16 x ^{2}}

\frac{\partial}{\partial y} (x^{2} sin (y))

\int_{1}^{7} \frac{4}{x ^{2}} d x

\int_{- 64}^{1} \frac{1}{x ^{\frac{1}{3}}} d x

\int sin (4 x - 2) sin (3 x + 5) d x

4 cos (3 x), 4 - 4 cos (3 x), [0, \frac{π}{3}]

What is (\partial)/(\partial x)(arcsin(4x)) ?
The answer to (\partial)/(\partial x)(arcsin(4x)) is 4/(sqrt(1-16x^2))