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Popular >

derivative of 4x^3ln(x+x^3)

Solution

\frac{d}{d x} (4 x^{3} ln (x) + x^{3})

Solution

12 x^{2} ln (x) + 7 x^{2}

Solution steps

\frac{d}{d x} (4 x^{3} ln (x) + x^{3})

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (4 x^{3} ln (x)) = 4 (3 x^{2} ln (x) + x^{2})

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

= 4 (3 x^{2} ln (x) + x^{2}) + 3 x^{2}

Simplify

4 (3 x^{2} ln (x) + x^{2}) + 3 x^{2} : 12 x^{2} ln (x) + 7 x^{2}

= 12 x^{2} ln (x) + 7 x^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of 4x^3ln(x+x^3) ?
The derivative of 4x^3ln(x+x^3) is 12x^2ln(x)+7x^2
What is the first derivative of 4x^3ln(x+x^3) ?
The first derivative of 4x^3ln(x+x^3) is 12x^2ln(x)+7x^2