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

The derivative of xln(x+(3x^2-2)^3) is ln(x)+1+18x(3x^2-2)^2

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

The first derivative of xln(x+(3x^2-2)^3) is ln(x)+1+18x(3x^2-2)^2

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

ln (x) + 1 + 18 x (3 x^{2} - 2)^{2}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} ((3 x^{2} - 2)^{3}) = 18 x (3 x^{2} - 2)^{2}

= ln (x) + 1 + 18 x (3 x^{2} - 2)^{2}

\int 2^{3 x + 4} d x

x \to 0 lim (cos (7 x))

x \to - 1 lim (3 - 2 x)

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

\frac{( 8 x ^{2} - 2 x - 9 )}{( 2 x - 3 )}

What is the derivative of xln(x+(3x^2-2)^3) ?
The derivative of xln(x+(3x^2-2)^3) is ln(x)+1+18x(3x^2-2)^2
What is the first derivative of xln(x+(3x^2-2)^3) ?
The first derivative of xln(x+(3x^2-2)^3) is ln(x)+1+18x(3x^2-2)^2