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

The derivative of x^2sqrt(x-4) is (5x^2-16x)/(2sqrt(x-4))

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

The first derivative of x^2sqrt(x-4) is (5x^2-16x)/(2sqrt(x-4))

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

\frac{5 x ^{2} - 16 x}{2 x - 4}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (x - 4) = \frac{1}{2 x - 4}

= 2 x x - 4 + \frac{1}{2 x - 4} x^{2}

Simplify

2 x x - 4 + \frac{1}{2 x - 4} x^{2} : \frac{5 x ^{2} - 16 x}{2 x - 4}

= \frac{5 x ^{2} - 16 x}{2 x - 4}

cos (x)

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

y = x^{3} (2 x + 3)^{7}

3 x, \frac{3}{x}, x = 3

\frac{d y}{d x} = - \frac{y}{x}

What is the derivative of x^2sqrt(x-4) ?
The derivative of x^2sqrt(x-4) is (5x^2-16x)/(2sqrt(x-4))
What is the first derivative of x^2sqrt(x-4) ?
The first derivative of x^2sqrt(x-4) is (5x^2-16x)/(2sqrt(x-4))