What is the derivative of x^2sqrt(6x-7) ?

The derivative of x^2sqrt(6x-7) is (15x^2-14x)/(sqrt(6x-7))

What is the first derivative of x^2sqrt(6x-7) ?

The first derivative of x^2sqrt(6x-7) is (15x^2-14x)/(sqrt(6x-7))

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\frac{d}{d x} (x^{2} 6 x - 7)

\frac{15 x ^{2} - 14 x}{6 x - 7}

Solution steps

\frac{d}{d x} (x^{2} 6 x - 7)

Apply the Product Rule:

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

f = x^{2}, g = 6 x - 7

= \frac{d}{d x} (x^{2}) 6 x - 7 + \frac{d}{d x} (6 x - 7) x^{2}

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

\frac{d}{d x} (6 x - 7) = \frac{3}{6 x - 7}

= 2 x 6 x - 7 + \frac{3}{6 x - 7} x^{2}

Simplify

2 x 6 x - 7 + \frac{3}{6 x - 7} x^{2} : \frac{15 x ^{2} - 14 x}{6 x - 7}

= \frac{15 x ^{2} - 14 x}{6 x - 7}

What is the derivative of x^2sqrt(6x-7) ?
The derivative of x^2sqrt(6x-7) is (15x^2-14x)/(sqrt(6x-7))
What is the first derivative of x^2sqrt(6x-7) ?
The first derivative of x^2sqrt(6x-7) is (15x^2-14x)/(sqrt(6x-7))