What is the derivative of f(x)=sqrt(3/2 x-5) ?

The derivative of f(x)=sqrt(3/2 x-5) is 3/(2sqrt(2)\sqrt{3x-10)}

What is the first derivative of f(x)=sqrt(3/2 x-5) ?

The first derivative of f(x)=sqrt(3/2 x-5) is 3/(2sqrt(2)\sqrt{3x-10)}

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derivative

\frac{3}{2 2 3 x - 10}

Solution steps

\frac{d}{d x} (\frac{3}{2} x - 5)

Apply the chain rule:

\frac{1}{2 \frac{3}{2} x - 5} \frac{d}{d x} (\frac{3}{2} x - 5)

= \frac{1}{2 \frac{3}{2} x - 5} \frac{d}{d x} (\frac{3}{2} x - 5)

\frac{d}{d x} (\frac{3}{2} x - 5) = \frac{3}{2}

= \frac{1}{2 \frac{3}{2} x - 5} \cdot \frac{3}{2}

Simplify

\frac{1}{2 \frac{3}{2} x - 5} \cdot \frac{3}{2} : \frac{3}{2 2 3 x - 10}

= \frac{3}{2 2 3 x - 10}

What is the derivative of f(x)=sqrt(3/2 x-5) ?
The derivative of f(x)=sqrt(3/2 x-5) is 3/(2sqrt(2)\sqrt{3x-10)}
What is the first derivative of f(x)=sqrt(3/2 x-5) ?
The first derivative of f(x)=sqrt(3/2 x-5) is 3/(2sqrt(2)\sqrt{3x-10)}