What is the derivative of x^2sqrt(6x-1) ?

The derivative of x^2sqrt(6x-1) is (15x^2-2x)/(sqrt(6x-1))

What is the first derivative of x^2sqrt(6x-1) ?

The first derivative of x^2sqrt(6x-1) is (15x^2-2x)/(sqrt(6x-1))

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\frac{d}{d x} (x^{2} 6 x - 1)

\frac{15 x ^{2} - 2 x}{6 x - 1}

Solution steps

\frac{d}{d x} (x^{2} 6 x - 1)

Apply the Product Rule:

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

f = x^{2}, g = 6 x - 1

= \frac{d}{d x} (x^{2}) 6 x - 1 + \frac{d}{d x} (6 x - 1) x^{2}

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

\frac{d}{d x} (6 x - 1) = \frac{3}{6 x - 1}

= 2 x 6 x - 1 + \frac{3}{6 x - 1} x^{2}

Simplify

2 x 6 x - 1 + \frac{3}{6 x - 1} x^{2} : \frac{15 x ^{2} - 2 x}{6 x - 1}

= \frac{15 x ^{2} - 2 x}{6 x - 1}

\int_{b}^{d} \frac{1}{r} d r

f (x) = 7 x^{3} + 5 x, at x = 7

\frac{d}{d x} (3 e^{x} (5 x^{5} - 2))

y^{'} = sin^{2} (x - y)

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

What is the derivative of x^2sqrt(6x-1) ?
The derivative of x^2sqrt(6x-1) is (15x^2-2x)/(sqrt(6x-1))
What is the first derivative of x^2sqrt(6x-1) ?
The first derivative of x^2sqrt(6x-1) is (15x^2-2x)/(sqrt(6x-1))