What is the derivative of x^2ln(x^3+1) ?

The derivative of x^2ln(x^3+1) is 2xln(x^3+1)+(3x^4)/(x^3+1)

What is the first derivative of x^2ln(x^3+1) ?

The first derivative of x^2ln(x^3+1) is 2xln(x^3+1)+(3x^4)/(x^3+1)

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\frac{d}{d x} (x^{2} ln (x^{3} + 1))

2 x ln (x^{3} + 1) + \frac{3 x ^{4}}{x ^{3} + 1}

Solution steps

\frac{d}{d x} (x^{2} ln (x^{3} + 1))

Apply the Product Rule:

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

f = x^{2}, g = ln (x^{3} + 1)

= \frac{d}{d x} (x^{2}) ln (x^{3} + 1) + \frac{d}{d x} (ln (x^{3} + 1)) x^{2}

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

\frac{d}{d x} (ln (x^{3} + 1)) = \frac{3 x ^{2}}{x ^{3} + 1}

= 2 x ln (x^{3} + 1) + \frac{3 x ^{2}}{x ^{3} + 1} x^{2}

\frac{3 x ^{2}}{x ^{3} + 1} x^{2} = \frac{3 x ^{4}}{x ^{3} + 1}

= 2 x ln (x^{3} + 1) + \frac{3 x ^{4}}{x ^{3} + 1}

\int (2 x^{2} - x)^{2} d x

\frac{d}{d x} ((x^{5} + 2)^{2} (x^{4} + 4)^{4})

f (x) = x^{4} - 32 x^{2} + 256, at x = - 1

\int arctan (7 x) d x

What is the derivative of x^2ln(x^3+1) ?
The derivative of x^2ln(x^3+1) is 2xln(x^3+1)+(3x^4)/(x^3+1)
What is the first derivative of x^2ln(x^3+1) ?
The first derivative of x^2ln(x^3+1) is 2xln(x^3+1)+(3x^4)/(x^3+1)