What is the derivative of 3x^5ln(x) ?

The derivative of 3x^5ln(x) is 3(5x^4ln(x)+x^4)

What is the first derivative of 3x^5ln(x) ?

The first derivative of 3x^5ln(x) is 3(5x^4ln(x)+x^4)

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\frac{d}{d x} (3 x^{5} ln (x))

3 (5 x^{4} ln (x) + x^{4})

Solution steps

\frac{d}{d x} (3 x^{5} ln (x))

Take the constant out:

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

= 3 \frac{d}{d x} (x^{5} ln (x))

Apply the Product Rule:

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

f = x^{5}, g = ln (x)

= 3 (\frac{d}{d x} (x^{5}) ln (x) + \frac{d}{d x} (ln (x)) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 3 (5 x^{4} ln (x) + \frac{1}{x} x^{5})

\frac{1}{x} x^{5} = x^{4}

= 3 (5 x^{4} ln (x) + x^{4})

What is the derivative of 3x^5ln(x) ?
The derivative of 3x^5ln(x) is 3(5x^4ln(x)+x^4)
What is the first derivative of 3x^5ln(x) ?
The first derivative of 3x^5ln(x) is 3(5x^4ln(x)+x^4)