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Popular >

derivative of sqrt(x)(x^2-1)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of sqrt((x+2^2*(x^2)/2))

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

derivative of (e^x/(5x^3))

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{3}})

tangent of f(x)=(1+5x)^{12},(0,1)tangent of

f (x) = (1 + 5 x)^{12}, (0, 1)

10y^'=10*9.81-5y

10 y^{^{'}} = 10 \cdot 9.81 - 5 y

tangent of y= 1/(x-1),\at x=6 tangent of

y = \frac{1}{x - 1}, at x = 6

Frequently Asked Questions (FAQ)

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