What is (\partial)/(\partial x)(sqrt((x+4)/(y+1))) ?

The answer to (\partial)/(\partial x)(sqrt((x+4)/(y+1))) is 1/(2sqrt(x+4)\sqrt{y+1)}

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(\partial)/(\partial x)(sqrt((x+4)/(y+1)))

\frac{\partial}{\partial x} (\frac{x + 4}{y + 1})

\frac{1}{2 x + 4 y + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{x + 4}{y + 1})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 \frac{x + 4}{y + 1}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 1})

= \frac{1}{2 \frac{x + 4}{y + 1}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 1})

\frac{\partial}{\partial x} (\frac{x + 4}{y + 1}) = \frac{1}{y + 1}

= \frac{1}{2 \frac{x + 4}{y + 1}} \cdot \frac{1}{y + 1}

Simplify

\frac{1}{2 \frac{x + 4}{y + 1}} \cdot \frac{1}{y + 1} : \frac{1}{2 x + 4 y + 1}

= \frac{1}{2 x + 4 y + 1}

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

\int cos^{3} (1) d x

f (x) = (3 x + 2) (4 x^{2} + 3)

\frac{\partial}{\partial x} (ln (x^{3} + y^{2}))

\frac{d}{d x} (sec (\frac{x}{2}))

What is (\partial)/(\partial x)(sqrt((x+4)/(y+1))) ?
The answer to (\partial)/(\partial x)(sqrt((x+4)/(y+1))) is 1/(2sqrt(x+4)\sqrt{y+1)}