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Popular >

derivative of 4x^3ln(x)

Solution

\frac{d}{d x} (4 x^{3} ln (x))

Solution

4 (3 x^{2} ln (x) + x^{2})

Solution steps

\frac{d}{d x} (4 x^{3} ln (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{3} ln (x))

Apply the Product Rule:

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

f = x^{3}, g = ln (x)

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

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

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

= 4 (3 x^{2} ln (x) + \frac{1}{x} x^{3})

\frac{1}{x} x^{3} = x^{2}

= 4 (3 x^{2} ln (x) + x^{2})

Popular Examples

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f (x) = 110 x - 16 x^{2}, at x = 3.438

integral of 6cos(sqrt(7x))

\int 6 cos (7 x) d x

derivative of e^{sin(x^2)}derivative of

e^{s i n (x^{2})}

limit as x approaches-infinity of (sqrt(2x^2+3))/(2x+3)

x \to - \infty lim (\frac{2 x ^{2} + 3}{2 x + 3})

limit as x approaches-1 of 3

x \to - 1 lim (3)

Frequently Asked Questions (FAQ)

What is the derivative of 4x^3ln(x) ?
The derivative of 4x^3ln(x) is 4(3x^2ln(x)+x^2)
What is the first derivative of 4x^3ln(x) ?
The first derivative of 4x^3ln(x) is 4(3x^2ln(x)+x^2)