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

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

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

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

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\frac{d}{d x} (x \cdot ln (x) + (3 \cdot 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}

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int 14 x^{\frac{3}{2}} d x

\int \frac{y ^{2}}{3} d y

(2 ln (x))^{^{'}}

\frac{d}{d x} (x^{3} e^{x^{3}})

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