What is the derivative of 3x^2ln(x+x^2) ?

The derivative of 3x^2ln(x+x^2) is 6xln(x)+5x

What is the first derivative of 3x^2ln(x+x^2) ?

The first derivative of 3x^2ln(x+x^2) is 6xln(x)+5x

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

6 x ln (x) + 5 x

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x^{2} ln (x)) + \frac{d}{d x} (x^{2})

\frac{d}{d x} (3 x^{2} ln (x)) = 3 (2 x ln (x) + x)

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

= 3 (2 x ln (x) + x) + 2 x

Simplify

3 (2 x ln (x) + x) + 2 x : 6 x ln (x) + 5 x

= 6 x ln (x) + 5 x

What is the derivative of 3x^2ln(x+x^2) ?
The derivative of 3x^2ln(x+x^2) is 6xln(x)+5x
What is the first derivative of 3x^2ln(x+x^2) ?
The first derivative of 3x^2ln(x+x^2) is 6xln(x)+5x