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Popular >

derivative of arccos(xy)

Solution

\frac{d}{d x} (arccos (x y))

Solution

- \frac{y + x \frac{d y}{d x}}{1 - x ^{2} y ^{2}}

Solution steps

\frac{d}{d x} (arccos (x y))

Apply the chain rule:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Simplify

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

= - \frac{y + x \frac{d y}{d x}}{1 - x ^{2} y ^{2}}

Popular Examples

derivative of \sqrt[5]{(3x^2+5x(1-x)^2})

\frac{d}{d x} (5 (3 x^{2} + 5 x) (1 - x)^{2})

derivative of 3/(x^3-4/(x^2))

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

derivative of x^5e^{7x}

\frac{d}{d x} (x^{5} e^{7 x})

limit as x approaches 1 of (x-1)^{3x-3}

x \to 1 lim ((x - 1)^{3 x - 3})

limit as x approaches 2 of xsqrt(13-x^2)

x \to 2 lim (x 13 - x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of arccos(xy) ?
The derivative of arccos(xy) is -(y+x\frac{dy)/(dx)}{sqrt(1-x^2y^2)}
What is the first derivative of arccos(xy) ?
The first derivative of arccos(xy) is -(y+x\frac{dy)/(dx)}{sqrt(1-x^2y^2)}