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Popular >

derivative of sqrt(x)(x-4^2)

Solution

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

Solution

\frac{5 x ^{2} - 24 x + 16}{2 x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

\frac{1}{2 x} (x - 4)^{2} + 2 (x - 4) x : \frac{5 x ^{2} - 24 x + 16}{2 x}

= \frac{5 x ^{2} - 24 x + 16}{2 x}

Popular Examples

(\partial)/(\partial x)(e^y+x+x^2+6)

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 6)

tangent of f(x)=(x^2+5)/(x-5),\at x=3 tangent of

f (x) = \frac{x ^{2} + 5}{x - 5}, at x = 3

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cos (\frac{x}{2})

limit as x approaches 0+of (1+6x)^{3/x}

x \to 0 + lim ((1 + 6 x)^{\frac{3}{x}})

(\partial)/(\partial t)(arctan(xsqrt(t)))

\frac{\partial}{\partial t} (arctan (x t))

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(x-4^2) ?
The derivative of sqrt(x)(x-4^2) is (5x^2-24x+16)/(2sqrt(x))
What is the first derivative of sqrt(x)(x-4^2) ?
The first derivative of sqrt(x)(x-4^2) is (5x^2-24x+16)/(2sqrt(x))