What is the derivative of f(x)=sqrt(1+8x) ?

The derivative of f(x)=sqrt(1+8x) is 4/(sqrt(1+8x))

What is the first derivative of f(x)=sqrt(1+8x) ?

The first derivative of f(x)=sqrt(1+8x) is 4/(sqrt(1+8x))

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derivative of

f (x) = 1 + 8 x

\frac{4}{1 + 8 x}

Solution steps

\frac{d}{d x} (1 + 8 x)

Apply the chain rule:

\frac{1}{2 1 + 8 x} \frac{d}{d x} (1 + 8 x)

= \frac{1}{2 1 + 8 x} \frac{d}{d x} (1 + 8 x)

\frac{d}{d x} (1 + 8 x) = 8

= \frac{1}{2 1 + 8 x} \cdot 8

Simplify

\frac{1}{2 1 + 8 x} \cdot 8 : \frac{4}{1 + 8 x}

= \frac{4}{1 + 8 x}

What is the derivative of f(x)=sqrt(1+8x) ?
The derivative of f(x)=sqrt(1+8x) is 4/(sqrt(1+8x))
What is the first derivative of f(x)=sqrt(1+8x) ?
The first derivative of f(x)=sqrt(1+8x) is 4/(sqrt(1+8x))