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Popular >

derivative of x^2sqrt(4x-1)

Solution

derivative of

x^{2} 4 x - 1

Solution

\frac{10 x ^{2} - 2 x}{4 x - 1}

Solution steps

\frac{d}{d x} (x^{2} 4 x - 1)

Apply the Product Rule:

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

f = x^{2}, g = 4 x - 1

= \frac{d}{d x} (x^{2}) 4 x - 1 + \frac{d}{d x} (4 x - 1) x^{2}

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

\frac{d}{d x} (4 x - 1) = \frac{2}{4 x - 1}

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

Simplify

2 x 4 x - 1 + \frac{2}{4 x - 1} x^{2} : \frac{10 x ^{2} - 2 x}{4 x - 1}

= \frac{10 x ^{2} - 2 x}{4 x - 1}

Popular Examples

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

\frac{d}{d x} ((4 x - 3)^{\frac{1}{2}})

limit as x approaches-2 of-x^3+x

x \to - 2 lim (- x^{3} + x)

tangent of f(x)= x/((1+x^2)),\at x=3 tangent of

f (x) = \frac{x}{( 1 + x ^{2} )}, at x = 3

integral from-3 to-1 of (x^2-4x+8)

\int_{- 3}^{- 1} (x^{2} - 4 x + 8) d x

limit as x approaches-1 of 3^{2x}

x \to - 1 lim (3^{2 x})

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(4x-1) ?
The derivative of x^2sqrt(4x-1) is (10x^2-2x)/(sqrt(4x-1))
What is the first derivative of x^2sqrt(4x-1) ?
The first derivative of x^2sqrt(4x-1) is (10x^2-2x)/(sqrt(4x-1))