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Popular >

derivative of arcsin((3x/4))

Solution

\frac{d}{d x} (arcsin (\frac{3 x}{4}))

Solution

\frac{3}{16 - 9 x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{3 x}{4}))

Apply the chain rule:

\frac{1}{1 - ( \frac{3 x}{4} ) ^{2}} \frac{d}{d x} (\frac{3 x}{4})

= \frac{1}{1 - ( \frac{3 x}{4} ) ^{2}} \frac{d}{d x} (\frac{3 x}{4})

\frac{d}{d x} (\frac{3 x}{4}) = \frac{3}{4}

= \frac{1}{1 - ( \frac{3 x}{4} ) ^{2}} \cdot \frac{3}{4}

Simplify

\frac{1}{1 - ( \frac{3 x}{4} ) ^{2}} \cdot \frac{3}{4} : \frac{3}{16 - 9 x ^{2}}

= \frac{3}{16 - 9 x ^{2}}

Popular Examples

(dx)/(dt)= 5/(xe^{t+5x)}

\frac{d x}{d t} = \frac{5}{x e ^{t + 5 x}}

integral from-5 to-2 of 4x^3

\int_{- 5}^{- 2} 4 x^{3} d x

(\partial)/(\partial x)(5x^2y^2)

\frac{\partial}{\partial x} (5 x^{2} y^{2})

derivative of f(x)=5cos^2(x)derivative of

f (x) = 5 cos^{2} (x)

limit as x approaches 4 of (x+4)/(x-3)

x \to 4 lim (\frac{x + 4}{x - 3})

Frequently Asked Questions (FAQ)

What is the derivative of arcsin((3x/4)) ?
The derivative of arcsin((3x/4)) is 3/(sqrt(16-9x^2))
What is the first derivative of arcsin((3x/4)) ?
The first derivative of arcsin((3x/4)) is 3/(sqrt(16-9x^2))