What is the derivative of x^3sqrt(2x-1) ?

The derivative of x^3sqrt(2x-1) is (7x^3-3x^2)/(sqrt(2x-1))

What is the first derivative of x^3sqrt(2x-1) ?

The first derivative of x^3sqrt(2x-1) is (7x^3-3x^2)/(sqrt(2x-1))

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

\frac{7 x ^{3} - 3 x ^{2}}{2 x - 1}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = 2 x - 1

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

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

Simplify

3 x^{2} 2 x - 1 + \frac{1}{2 x - 1} x^{3} : \frac{7 x ^{3} - 3 x ^{2}}{2 x - 1}

= \frac{7 x ^{3} - 3 x ^{2}}{2 x - 1}

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

y = - 9 x^{2}, at x = 8

y^{^{''}} = x^{2} + 1

y = 1 + (2 x + 1)^{8}

\int (x^{2} + 1) n x d x

What is the derivative of x^3sqrt(2x-1) ?
The derivative of x^3sqrt(2x-1) is (7x^3-3x^2)/(sqrt(2x-1))
What is the first derivative of x^3sqrt(2x-1) ?
The first derivative of x^3sqrt(2x-1) is (7x^3-3x^2)/(sqrt(2x-1))