What is the derivative of x^2sqrt(10x-3) ?

The derivative of x^2sqrt(10x-3) is (25x^2-6x)/(sqrt(10x-3))

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

The first derivative of x^2sqrt(10x-3) is (25x^2-6x)/(sqrt(10x-3))

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\frac{d}{d x} (x^{2} 10 x - 3)

\frac{25 x ^{2} - 6 x}{10 x - 3}

Solution steps

\frac{d}{d x} (x^{2} 10 x - 3)

Apply the Product Rule:

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

f = x^{2}, g = 10 x - 3

= \frac{d}{d x} (x^{2}) 10 x - 3 + \frac{d}{d x} (10 x - 3) x^{2}

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

\frac{d}{d x} (10 x - 3) = \frac{5}{10 x - 3}

= 2 x 10 x - 3 + \frac{5}{10 x - 3} x^{2}

Simplify

2 x 10 x - 3 + \frac{5}{10 x - 3} x^{2} : \frac{25 x ^{2} - 6 x}{10 x - 3}

= \frac{25 x ^{2} - 6 x}{10 x - 3}

What is the derivative of x^2sqrt(10x-3) ?
The derivative of x^2sqrt(10x-3) is (25x^2-6x)/(sqrt(10x-3))
What is the first derivative of x^2sqrt(10x-3) ?
The first derivative of x^2sqrt(10x-3) is (25x^2-6x)/(sqrt(10x-3))