What is the derivative of sqrt(3+2f(x)) ?

The derivative of sqrt(3+2f(x)) is x/(sqrt(3+2fx))

What is the first derivative of sqrt(3+2f(x)) ?

The first derivative of sqrt(3+2f(x)) is x/(sqrt(3+2fx))

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derivative of

3 + 2 f (x)

\frac{x}{3 + 2 f x}

Solution steps

\frac{d}{df} (3 + 2 f x)

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 3 + 2 f x} \frac{d}{df} (3 + 2 f x)

= \frac{1}{2 3 + 2 f x} \frac{d}{df} (3 + 2 f x)

\frac{d}{df} (3 + 2 f x) = 2 x

= \frac{1}{2 3 + 2 f x} \cdot 2 x

Simplify

\frac{1}{2 3 + 2 f x} \cdot 2 x : \frac{x}{3 + 2 f x}

= \frac{x}{3 + 2 f x}

What is the derivative of sqrt(3+2f(x)) ?
The derivative of sqrt(3+2f(x)) is x/(sqrt(3+2fx))
What is the first derivative of sqrt(3+2f(x)) ?
The first derivative of sqrt(3+2f(x)) is x/(sqrt(3+2fx))