What is the derivative of x^2sqrt(4x-3) ?

The derivative of x^2sqrt(4x-3) is (10x^2-6x)/(sqrt(4x-3))

What is the first derivative of x^2sqrt(4x-3) ?

The first derivative of x^2sqrt(4x-3) is (10x^2-6x)/(sqrt(4x-3))

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

\frac{10 x ^{2} - 6 x}{4 x - 3}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = 4 x - 3

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

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

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

= 2 x 4 x - 3 + \frac{2}{4 x - 3} x^{2}

Simplify

2 x 4 x - 3 + \frac{2}{4 x - 3} x^{2} : \frac{10 x ^{2} - 6 x}{4 x - 3}

= \frac{10 x ^{2} - 6 x}{4 x - 3}

x \to 4 - lim (x^{2} + 2)

x \to 0 - lim (\frac{2}{9 x ^{\frac{1}{3}}})

y^{^{'}} = (x + y - 4) 2

f (x) = 2 - 6 x

What is the derivative of x^2sqrt(4x-3) ?
The derivative of x^2sqrt(4x-3) is (10x^2-6x)/(sqrt(4x-3))
What is the first derivative of x^2sqrt(4x-3) ?
The first derivative of x^2sqrt(4x-3) is (10x^2-6x)/(sqrt(4x-3))