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Popular Calculus >

derivative of 4x^4ln(x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{4}, g = ln (x)

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

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

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

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

\frac{1}{x} x^{4} = x^{3}

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

Graph

Popular Examples

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limit as x approaches infinity of-3/x

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

y^'+3(tan(3x))y=-2cos(3x)

y^{^{'}} + 3 (tan (3 x)) y = - 2 cos (3 x)

Frequently Asked Questions (FAQ)

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