What is the derivative of (x^4/4 ln(x)-(x^4)/(16)) ?

The derivative of (x^4/4 ln(x)-(x^4)/(16)) is x^3ln(x)

What is the first derivative of (x^4/4 ln(x)-(x^4)/(16)) ?

The first derivative of (x^4/4 ln(x)-(x^4)/(16)) is x^3ln(x)

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\frac{d}{d x} (\frac{x ^{4}}{4} ln (x) - \frac{x ^{4}}{16})

x^{3} ln (x)

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{4} ln (x) - \frac{x ^{4}}{16})

Simplify

\frac{x ^{4}}{4} ln (x) - \frac{x ^{4}}{16} : \frac{x ^{4} ln ( x )}{4} - \frac{x ^{4}}{16}

= \frac{d}{d x} (\frac{x ^{4} ln ( x )}{4} - \frac{x ^{4}}{16})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{4} ln ( x )}{4}) - \frac{d}{d x} (\frac{x ^{4}}{16})

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

\frac{d}{d x} (\frac{x ^{4}}{16}) = \frac{x ^{3}}{4}

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

Simplify

= x^{3} ln (x)

x \to - \infty lim (x + x^{3})

s l o p e in t erce pt (1.2) (4.4)

\int \frac{x ^{3}}{x ^{2} - 81} d x

d er i v a t i v e y (θ) = \frac{sin ( θ )}{5} + \frac{c}{θ}

\int (\frac{x - 1}{x})^{2} d x

What is the derivative of (x^4/4 ln(x)-(x^4)/(16)) ?
The derivative of (x^4/4 ln(x)-(x^4)/(16)) is x^3ln(x)
What is the first derivative of (x^4/4 ln(x)-(x^4)/(16)) ?
The first derivative of (x^4/4 ln(x)-(x^4)/(16)) is x^3ln(x)