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Popular >

derivative of x^2sqrt(x-1)

Solution

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

Solution

\frac{5 x ^{2} - 4 x}{2 x - 1}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = x - 1

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Simplify

2 x x - 1 + \frac{1}{2 x - 1} x^{2} : \frac{5 x ^{2} - 4 x}{2 x - 1}

= \frac{5 x ^{2} - 4 x}{2 x - 1}

Popular Examples

integral of (3x^2+8x-12)/(x^3+7x+12x)

\int \frac{3 x ^{2} + 8 x - 12}{x ^{3} + 7 x + 12 x} d x

integral of (3^{x+2})/(4^{x-1)}

\int \frac{3 ^{x + 2}}{4 ^{x - 1}} d x

integral of xcos(6x)

\int x cos (6 x) d x

integral of ((26))/((x-1)(x^2+25))

\int \frac{( 26 )}{( x - 1 ) ( x ^{2} + 25 )} d x

integral of x^{-2}e^{1/x}

\int x^{- 2} e^{\frac{1}{x}} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(x-1) ?
The derivative of x^2sqrt(x-1) is (5x^2-4x)/(2sqrt(x-1))
What is the first derivative of x^2sqrt(x-1) ?
The first derivative of x^2sqrt(x-1) is (5x^2-4x)/(2sqrt(x-1))