What is the derivative of 2xln(4x^2) ?

The derivative of 2xln(4x^2) is 2(2ln(2x)+2)

What is the first derivative of 2xln(4x^2) ?

The first derivative of 2xln(4x^2) is 2(2ln(2x)+2)

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\frac{d}{d x} (2 x ln (4 x^{2}))

2 (2 ln (2 x) + 2)

Solution steps

\frac{d}{d x} (2 x ln (4 x^{2}))

Take the constant out:

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

= 2 \frac{d}{d x} (x ln (4 x^{2}))

Apply the Product Rule:

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

f = x, g = ln (4 x^{2})

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

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (4 x^{2})) = \frac{2}{x}

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

Simplify

2 (1 \cdot ln (4 x^{2}) + \frac{2}{x} x) : 2 (2 ln (2 x) + 2)

= 2 (2 ln (2 x) + 2)

\int \frac{60}{2 x + 5} - 5 d x

\int cot (x) (- 8 sin (x) - 10 csc (x)) d x

y^{2} + x^{2} y^{^{'}} = 0

\int x (x + 2)^{- \frac{3}{2}} d x

\int e^{c o s (4 x)} sin (4 x) d x

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