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Popular >

derivative of xsqrt(x-1)

Solution

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

Solution

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

Solution steps

\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{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}

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

Simplify

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

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

Popular Examples

derivative of y= x/((x-2)^2)derivative of

y = \frac{x}{( x - 2 ) ^{2}}

derivative of (x^2+1*(x+5+1/x))

\frac{d}{d x} ((x^{2} + 1) \cdot (x + 5 + \frac{1}{x}))

derivative of 3sin(x+1)

\frac{d}{d x} (3 sin (x) + 1)

(dy)/(dx)=e^{5x+4y}

\frac{d y}{d x} = e^{5 x + 4 y}

integral from 2 to infinity of 9/(2x^2)

\int_{2}^{\infty} \frac{9}{2 x ^{2}} d x

Frequently Asked Questions (FAQ)

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