What is implicit tan(x/y)=x+y ?

The answer to implicit tan(x/y)=x+y is (dy)/(dx)=-(y^2-ysec^2(x/y))/(y^2+xsec^2(x/y))

Popular >

implicit tan(x/y)=x+y

implicit derivative

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

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

f (x) = arctan (\frac{x}{2}), at x = 2

2 x + 6, - 2, 2

y = ln (x^{2} - 2 x + 1), (2, 0)

\frac{d}{d x} (2^{s i n (x)})

\int_{0}^{4} \frac{ln ( x )}{x} d x

What is implicit tan(x/y)=x+y ?
The answer to implicit tan(x/y)=x+y is (dy)/(dx)=-(y^2-ysec^2(x/y))/(y^2+xsec^2(x/y))