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Popular >

derivative of x^4ln(x-1/3 x^3)

Solution

\frac{d}{d x} (x^{4} ln (x) - \frac{1}{3} x^{3})

Solution

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

Solution steps

\frac{d}{d x} (x^{4} ln (x) - \frac{1}{3} x^{3})

Simplify

x^{4} ln (x) - \frac{1}{3} x^{3} : x^{4} ln (x) - \frac{x ^{3}}{3}

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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