What is the derivative of f(x)=((xsqrt(x-1))/2) ?

The derivative of f(x)=((xsqrt(x-1))/2) is (3x-2)/(4sqrt(x-1))

What is the first derivative of f(x)=((xsqrt(x-1))/2) ?

The first derivative of f(x)=((xsqrt(x-1))/2) is (3x-2)/(4sqrt(x-1))

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derivative of

f (x) = (\frac{x x - 1}{2})

\frac{3 x - 2}{4 x - 1}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x - 1

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

\frac{d x}{d x} = 1

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

= \frac{1}{2} (1 \cdot x - 1 + \frac{1}{2 x - 1} x)

Simplify

\frac{1}{2} (1 \cdot x - 1 + \frac{1}{2 x - 1} x) : \frac{3 x - 2}{4 x - 1}

= \frac{3 x - 2}{4 x - 1}

m (r) = \frac{r ^{3} + 3 r + 2}{r ^{2} - 1}

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

- 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}

f (x) = xx

f (x) = x - 1

What is the derivative of f(x)=((xsqrt(x-1))/2) ?
The derivative of f(x)=((xsqrt(x-1))/2) is (3x-2)/(4sqrt(x-1))
What is the first derivative of f(x)=((xsqrt(x-1))/2) ?
The first derivative of f(x)=((xsqrt(x-1))/2) is (3x-2)/(4sqrt(x-1))