What is the derivative of 6x^4ln(x) ?

The derivative of 6x^4ln(x) is 6(4x^3ln(x)+x^3)

What is the first derivative of 6x^4ln(x) ?

The first derivative of 6x^4ln(x) is 6(4x^3ln(x)+x^3)

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derivative of

6 x^{4} ln (x)

6 (4 x^{3} ln (x) + x^{3})

Solution steps

\frac{d}{d x} (6 x^{4} ln (x))

Take the constant out:

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

= 6 \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)

= 6 (\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}

= 6 (4 x^{3} ln (x) + \frac{1}{x} x^{4})

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

= 6 (4 x^{3} ln (x) + x^{3})

x \to 2 - lim (x)

\frac{d}{d x} (sin (20 x))

\frac{d}{d x} ((x^{2} - 5)^{2})

16 x

\int \frac{12 ln ( x )}{x} d x

What is the derivative of 6x^4ln(x) ?
The derivative of 6x^4ln(x) is 6(4x^3ln(x)+x^3)
What is the first derivative of 6x^4ln(x) ?
The first derivative of 6x^4ln(x) is 6(4x^3ln(x)+x^3)