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

The answer to (\partial)/(\partial x)(sqrt(1+x)) is 1/(2sqrt(1+x))

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

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

\frac{1}{2 1 + x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int_{- 5}^{5} 10 d x

tan^{2} (7 x)

\int_{0}^{\frac{π}{2}} 5 sec^{4} (\frac{t}{2}) d t

\int \frac{- 1200 x}{25 - x ^{2}} d x

3.23 e^{- 61.4 t}

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