What is the derivative of f(y)=6x^2ln(x^2) ?

The derivative of f(y)=6x^2ln(x^2) is 6(2xln(x^2)+2x)

What is the first derivative of f(y)=6x^2ln(x^2) ?

The first derivative of f(y)=6x^2ln(x^2) is 6(2xln(x^2)+2x)

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derivative of

f (y) = 6 x^{2} ln (x^{2})

6 (2 x ln (x^{2}) + 2 x)

Solution steps

\frac{d}{d x} (6 x^{2} ln (x^{2}))

Take the constant out:

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

= 6 \frac{d}{d x} (x^{2} ln (x^{2}))

Apply the Product Rule:

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

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

= 6 (\frac{d}{d x} (x^{2}) ln (x^{2}) + \frac{d}{d x} (ln (x^{2})) x^{2})

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

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

= 6 (2 x ln (x^{2}) + \frac{2}{x} x^{2})

\frac{2}{x} x^{2} = 2 x

= 6 (2 x ln (x^{2}) + 2 x)

What is the derivative of f(y)=6x^2ln(x^2) ?
The derivative of f(y)=6x^2ln(x^2) is 6(2xln(x^2)+2x)
What is the first derivative of f(y)=6x^2ln(x^2) ?
The first derivative of f(y)=6x^2ln(x^2) is 6(2xln(x^2)+2x)