What is the derivative of (x^6/(12)ln(x)-(x^6)/(72)) ?

The derivative of (x^6/(12)ln(x)-(x^6)/(72)) is (x^5ln(x))/2

What is the first derivative of (x^6/(12)ln(x)-(x^6)/(72)) ?

The first derivative of (x^6/(12)ln(x)-(x^6)/(72)) is (x^5ln(x))/2

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\frac{d}{d x} (\frac{x ^{6}}{12} ln (x) - \frac{x ^{6}}{72})

\frac{x ^{5} ln ( x )}{2}

Solution steps

\frac{d}{d x} (\frac{x ^{6}}{12} ln (x) - \frac{x ^{6}}{72})

Simplify

\frac{x ^{6}}{12} ln (x) - \frac{x ^{6}}{72} : \frac{x ^{6} ln ( x )}{12} - \frac{x ^{6}}{72}

= \frac{d}{d x} (\frac{x ^{6} ln ( x )}{12} - \frac{x ^{6}}{72})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{6} ln ( x )}{12}) - \frac{d}{d x} (\frac{x ^{6}}{72})

\frac{d}{d x} (\frac{x ^{6} ln ( x )}{12}) = \frac{1}{12} (6 x^{5} ln (x) + x^{5})

\frac{d}{d x} (\frac{x ^{6}}{72}) = \frac{x ^{5}}{12}

= \frac{1}{12} (6 x^{5} ln (x) + x^{5}) - \frac{x ^{5}}{12}

Simplify

\frac{1}{12} (6 x^{5} ln (x) + x^{5}) - \frac{x ^{5}}{12} : \frac{x ^{5} ln ( x )}{2}

= \frac{x ^{5} ln ( x )}{2}

\frac{d}{d x} (e^{- 5 x} - 5 e^{- 5 x} x)

\frac{d}{d x} (x \cdot e^{- 2 x})

\frac{d}{d x} (\frac{x}{( ∣ y ∣ - ∣ z ∣ )})

\int \frac{x ^{4} + x ^{2} + 1}{x - 1} d x

\frac{d}{d x} (sin (x) - 3 cos (x))

What is the derivative of (x^6/(12)ln(x)-(x^6)/(72)) ?
The derivative of (x^6/(12)ln(x)-(x^6)/(72)) is (x^5ln(x))/2
What is the first derivative of (x^6/(12)ln(x)-(x^6)/(72)) ?
The first derivative of (x^6/(12)ln(x)-(x^6)/(72)) is (x^5ln(x))/2