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Popular >

implicit xy=cot(xy)

Solution

implicit derivative

x y = cot (x y)

Solution

\frac{d y}{d x} = - \frac{y}{x}

Solution steps

x y = cot (x y)

Treat

y

as

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y}{x}

\frac{d y}{d x} = - \frac{y}{x}

Popular Examples

integral of x/((z^2+x^2)^{3/2)}

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

derivative of y= 3/x derivative of

y = \frac{3}{x}

integral of (6)

\int (6) d x

(\partial)/(\partial t)(3sqrt(s^2+t^2))

\frac{\partial}{\partial t} (3 s^{2} + t^{2})

integral from 0 to 3 of xe^{x/2}

\int_{0}^{3} x e^{\frac{x}{2}} d x

Frequently Asked Questions (FAQ)

What is implicit xy=cot(xy) ?
The answer to implicit xy=cot(xy) is (dy)/(dx)=-y/x