What is the derivative of sqrt(x-1)(x^2+1) ?

The derivative of sqrt(x-1)(x^2+1) is (5x^2-4x+1)/(2sqrt(x-1))

What is the first derivative of sqrt(x-1)(x^2+1) ?

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

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derivative of

x - 1 (x^{2} + 1)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

x \to 0 + lim (6 - \frac{1}{x ^{3}})

t^{2} y^{^{''}} - 8 t y^{^{'}} + 8 y = 0

\int 6 x ln (x) d x

sin (t^{2})

\int t e^{- i 2 π f t} d t

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