What is the derivative of arccos(x^2+3/2 x) ?

The derivative of arccos(x^2+3/2 x) is -(4x+3)/(sqrt(4-4x^4-12x^3-9x^2))

What is the first derivative of arccos(x^2+3/2 x) ?

The first derivative of arccos(x^2+3/2 x) is -(4x+3)/(sqrt(4-4x^4-12x^3-9x^2))

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derivative of

arccos (x^{2} + \frac{3}{2} x)

- \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

Solution steps

\frac{d}{d x} (arccos (x^{2} + \frac{3}{2} x))

Simplify

arccos (x^{2} + \frac{3}{2} x) : arccos (x^{2} + \frac{3 x}{2})

= \frac{d}{d x} (arccos (x^{2} + \frac{3 x}{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2} + \frac{3 x}{2}) = 2 x + \frac{3}{2}

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

Simplify

- \frac{1}{1 - ( x ^{2} + \frac{3 x}{2} ) ^{2}} (2 x + \frac{3}{2}) : - \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

= - \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

\frac{d}{d x} (e^{- 8 x} cos (8 x))

n = 0 \sum \infty e^{- n - 1}

\frac{\partial}{\partial y} (8 x^{2} + 7 y^{2} + 2)

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

What is the derivative of arccos(x^2+3/2 x) ?
The derivative of arccos(x^2+3/2 x) is -(4x+3)/(sqrt(4-4x^4-12x^3-9x^2))
What is the first derivative of arccos(x^2+3/2 x) ?
The first derivative of arccos(x^2+3/2 x) is -(4x+3)/(sqrt(4-4x^4-12x^3-9x^2))