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)

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

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})

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

y^{^{'}} = x - x^{2}

f (x) = 10 x + ln (10 x)

y = x^{3} - 9 x, (3, 0)

f (x) = x - 5

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)