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Popular >

derivative of arcsin(x/a)

Solution

derivative of

arcsin (\frac{x}{a})

Solution

\frac{a ^{2}}{a a ^{2} - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{a}) = \frac{1}{a}

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

Simplify

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

= \frac{a ^{2}}{a a ^{2} - x ^{2}}

Popular Examples

derivative of (4/3)pix^3 derivative of

(\frac{4}{3}) π x^{3}

derivative of 4xy^2-x^2y^2-xy^3

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

integral of-1/2 x^{1/2}

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

tangent of f(x)=-3x^2+3x+1,\at x=1 tangent of

f (x) = - 3 x^{2} + 3 x + 1, at x = 1

derivative of y= 2/(1-9x^2)derivative of

y = \frac{2}{1 - 9 x ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(x/a) ?
The derivative of arcsin(x/a) is (sqrt(a^2))/(asqrt(a^2-x^2))
What is the first derivative of arcsin(x/a) ?
The first derivative of arcsin(x/a) is (sqrt(a^2))/(asqrt(a^2-x^2))